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Systems of Equations: Classroom Packet

Grade 8 Algebra: Checking Solutions of Systems

Name: ______________________Date: ____________Score: ____ / 8

Level 1

Simple systems

  1. 1. Is the ordered pair a solution of the system:
    {x+y=5x−y=1(3,2)\begin{cases} x + y = 5 \\ x - y = 1 \end{cases}\quad (3, 2)
  2. 2. Is the ordered pair a solution of the system:
    {x+y=7x−y=3(5,2)\begin{cases} x + y = 7 \\ x - y = 3 \end{cases}\quad (5, 2)
  3. 3. Is the ordered pair a solution of the system:
    {x+y=6x−y=2(3,3)\begin{cases} x + y = 6 \\ x - y = 2 \end{cases}\quad (3, 3)
  4. 4. Is the ordered pair a solution of the system:
    {y=2xx+y=9(3,6)\begin{cases} y = 2x \\ x + y = 9 \end{cases}\quad (3, 6)
  5. 5. Is the ordered pair a solution of the system:
    {y=x+1x+y=7(3,4)\begin{cases} y = x + 1 \\ x + y = 7 \end{cases}\quad (3, 4)
  6. 6. Is the ordered pair a solution of the system:
    {y=3xx+y=8(2,5)\begin{cases} y = 3x \\ x + y = 8 \end{cases}\quad (2, 5)
  7. 7. Is the ordered pair a solution of the system:
    {x+y=10x−y=4(7,3)\begin{cases} x + y = 10 \\ x - y = 4 \end{cases}\quad (7, 3)
  8. 8. Is the ordered pair a solution of the system:
    {y=x−2x+y=6(5,3)\begin{cases} y = x - 2 \\ x + y = 6 \end{cases}\quad (5, 3)

Answer Key

Level 1

  1. 1. Yes\text{Yes}
  2. 2. Yes\text{Yes}
  3. 3. No\text{No}
  4. 4. Yes\text{Yes}
  5. 5. Yes\text{Yes}
  6. 6. No\text{No}
  7. 7. Yes\text{Yes}
  8. 8. No\text{No}

Grade 8 Algebra: Checking Solutions of Systems

Name: ______________________Date: ____________Score: ____ / 8

Level 2

Negatives and coefficients

  1. 1. Is the ordered pair a solution of the system:
    {2x+y=4x−y=5(3,−2)\begin{cases} 2x + y = 4 \\ x - y = 5 \end{cases}\quad (3, -2)
  2. 2. Is the ordered pair a solution of the system:
    {3x−y=7x+2y=0(2,−1)\begin{cases} 3x - y = 7 \\ x + 2y = 0 \end{cases}\quad (2, -1)
  3. 3. Is the ordered pair a solution of the system:
    {y=−x+1y=2x−5(2,−1)\begin{cases} y = -x + 1 \\ y = 2x - 5 \end{cases}\quad (2, -1)
  4. 4. Is the ordered pair a solution of the system:
    {2x+3y=1x−y=3(−1,1)\begin{cases} 2x + 3y = 1 \\ x - y = 3 \end{cases}\quad (-1, 1)
  5. 5. Is the ordered pair a solution of the system:
    {y=4x+3y=−x−2(−1,−1)\begin{cases} y = 4x + 3 \\ y = -x - 2 \end{cases}\quad (-1, -1)
  6. 6. Is the ordered pair a solution of the system:
    {4x−y=92x+y=3(1,−5)\begin{cases} 4x - y = 9 \\ 2x + y = 3 \end{cases}\quad (1, -5)
  7. 7. Is the ordered pair a solution of the system:
    {x+4y=−63x−y=8(2,−2)\begin{cases} x + 4y = -6 \\ 3x - y = 8 \end{cases}\quad (2, -2)
  8. 8. Is the ordered pair a solution of the system:
    {5x+2y=4x−y=−3(0,2)\begin{cases} 5x + 2y = 4 \\ x - y = -3 \end{cases}\quad (0, 2)

Answer Key

Level 2

  1. 1. Yes\text{Yes}
  2. 2. Yes\text{Yes}
  3. 3. Yes\text{Yes}
  4. 4. No\text{No}
  5. 5. Yes\text{Yes}
  6. 6. No\text{No}
  7. 7. Yes\text{Yes}
  8. 8. No\text{No}

Grade 8 Algebra: Checking Solutions of Systems

Name: ______________________Date: ____________Score: ____ / 8

Level 3

Choosing the solution

  1. 1. Which ordered pair is the solution:
    {y=−3x+7y=x−1(1,4), (2,1), (3,−2)\begin{cases} y = -3x + 7 \\ y = x - 1 \end{cases}\quad (1, 4),\ (2, 1),\ (3, -2)
  2. 2. Which ordered pair is the solution:
    {2x+y=8x−y=1(2,4), (4,0), (3,2)\begin{cases} 2x + y = 8 \\ x - y = 1 \end{cases}\quad (2, 4),\ (4, 0),\ (3, 2)
  3. 3. Which ordered pair is the solution:
    {x+y=−12x−y=−8(1,−2), (−3,2), (−2,1)\begin{cases} x + y = -1 \\ 2x - y = -8 \end{cases}\quad (1, -2),\ (-3, 2),\ (-2, 1)
  4. 4. Which ordered pair is the solution:
    {y=12x+1y=−x+4(4,3), (0,1), (2,2)\begin{cases} y = \tfrac{1}{2}x + 1 \\ y = -x + 4 \end{cases}\quad (4, 3),\ (0, 1),\ (2, 2)
  5. 5. Which ordered pair is the solution:
    {3x+2y=12x−2y=−4(4,0), (2,3), (0,2)\begin{cases} 3x + 2y = 12 \\ x - 2y = -4 \end{cases}\quad (4, 0),\ (2, 3),\ (0, 2)
  6. 6. Find k so that (2, k) is a solution:
    {y=3x−1y=x+3\begin{cases} y = 3x - 1 \\ y = x + 3 \end{cases}
  7. 7. Is the ordered pair a solution of the system:
    {2x+y=54x−y=4(1.5,2)\begin{cases} 2x + y = 5 \\ 4x - y = 4 \end{cases}\quad (1.5, 2)
  8. 8. Is the ordered pair a solution of the system:
    {4x+y=52x−y=−1(12,3)\begin{cases} 4x + y = 5 \\ 2x - y = -1 \end{cases}\quad (\tfrac{1}{2}, 3)

Answer Key

Level 3

  1. 1. (2,1)(2, 1)
  2. 2. (3,2)(3, 2)
  3. 3. (−3,2)(-3, 2)
  4. 4. (2,2)(2, 2)
  5. 5. (2,3)(2, 3)
  6. 6. k=5k = 5
  7. 7. Yes\text{Yes}
  8. 8. No\text{No}

Grade 8 Algebra: Solving Systems by Graphing

Name: ______________________Date: ____________Score: ____ / 8

Level 1

Lines crossing in the first quadrant

Directions: The solution is the point where the two lines cross. Write it as an ordered pair (x,y){(x, y)}.

  1. 1. Find the solution of the system:
    1122334455667788xy
  2. 2. Find the solution of the system:
    112233445566778899xy
  3. 3. Find the solution of the system:
    1122334455667788xy
  4. 4. Find the solution of the system:
    112233445566778899xy
  5. 5. Find the solution of the system:
    112233445566778899xy
  6. 6. Find the solution of the system:
    112233445566778899xy
  7. 7. Find the solution of the system:
    112233445566778899xy
  8. 8. Find the solution of the system:
    112233445566778899xy

Answer Key

Level 1

  1. 1. (3,4)(3, 4)
  2. 2. (2,4)(2, 4)
  3. 3. (3,3)(3, 3)
  4. 4. (4,3)(4, 3)
  5. 5. (5,2)(5, 2)
  6. 6. (4,4)(4, 4)
  7. 7. (3,4)(3, 4)
  8. 8. (1,4)(1, 4)

Grade 8 Algebra: Solving Systems by Graphing

Name: ______________________Date: ____________Score: ____ / 8

Level 2

All four quadrants and special cases

Directions: The solution is the point where the two lines cross. Write it as an ordered pair (x,y){(x, y)}.

  1. 1. Find the solution of the system:
    −5−5−4−4−3−3−2−2−1−11122334455xy
  2. 2. Find the solution of the system:
    −5−5−4−4−3−3−2−2−1−11122334455xy
  3. 3. Find the solution of the system:
    −6−6−5−5−4−4−3−3−2−2−1−1112233445566xy
  4. 4. Find the solution of the system:
    −5−5−4−4−3−3−2−2−1−11122334455xy
  5. 5. Find the solution of the system:
    −5−5−4−4−3−3−2−2−1−11122334455xy
  6. 6. Find the solution of the system:
    −5−5−4−4−3−3−2−2−1−11122334455xy
  7. 7. Find the solution of the system:
    −5−5−4−4−3−3−2−2−1−11122334455xy
  8. 8. Find the solution of the system:
    −5−5−4−4−3−3−2−2−1−11122334455xy

Answer Key

Level 2

  1. 1. (1,−1)(1, -1)
  2. 2. (−2,−1)(-2, -1)
  3. 3. (2,−3)(2, -3)
  4. 4. (−2,−3)(-2, -3)
  5. 5. No solution\text{No solution}
  6. 6. (2,0)(2, 0)
  7. 7. (−3,4)(-3, 4)
  8. 8. Infinitely many\text{Infinitely many}

Grade 8 Algebra: Solving Systems by Graphing

Name: ______________________Date: ____________Score: ____ / 8

Level 3

Write the equations, then solve

Directions: The solution is the point where the two lines cross. Write it as an ordered pair (x,y){(x, y)}.

  1. 1. Write each line's equation, then give the solution:
    112233445566778899xy
  2. 2. Write each line's equation, then give the solution:
    −5−5−4−4−3−3−2−2−1−11122334455xy
  3. 3. Write each line's equation, then give the solution:
    −5−5−4−4−3−3−2−2−1−11122334455xy
  4. 4. Write each line's equation, then give the solution:
    −5−5−4−4−3−3−2−2−1−11122334455xy
  5. 5. Write each line's equation, then give the solution:
    −5−5−4−4−3−3−2−2−1−11122334455xy
  6. 6. Write each line's equation, then give the solution:
    −5−5−4−4−3−3−2−2−1−11122334455xy
  7. 7. Write each line's equation, then give the solution:
    −5−5−4−4−3−3−2−2−1−1112233445566xy
  8. 8. Write each line's equation, then give the solution:
    −5−5−4−4−3−3−2−2−1−11122334455xy

Answer Key

Level 3

  1. 1. y=2x+2, y=−x+5; (1,4)y = 2x + 2,\ y = -x + 5;\ (1, 4)
  2. 2. y=2x−3, y=−x+3; (2,1)y = 2x - 3,\ y = -x + 3;\ (2, 1)
  3. 3. y=−12x+4, y=x−2; (4,2)y = -\tfrac{1}{2}x + 4,\ y = x - 2;\ (4, 2)
  4. 4. y=2x+4, y=−x+1; (−1,2)y = 2x + 4,\ y = -x + 1;\ (-1, 2)
  5. 5. y=−x, y=x−4; (2,−2)y = -x,\ y = x - 4;\ (2, -2)
  6. 6. y=13x+1, y=3x−3; (1.5,1.5)y = \tfrac{1}{3}x + 1,\ y = 3x - 3;\ (1.5, 1.5)
  7. 7. y=3, y=2x+1; (1,3)y = 3,\ y = 2x + 1;\ (1, 3)
  8. 8. y=12x−1, y=12x+2; No solutiony = \tfrac{1}{2}x - 1,\ y = \tfrac{1}{2}x + 2;\ \text{No solution}

Grade 8 Algebra: Solving Systems by Substitution

Name: ______________________Date: ____________Score: ____ / 8

Level 1

One variable already isolated

  1. 1. Solve by substitution:
    {y=2xx+y=12\begin{cases} y = 2x \\ x + y = 12 \end{cases}
  2. 2. Solve by substitution:
    {y=x+3x+y=9\begin{cases} y = x + 3 \\ x + y = 9 \end{cases}
  3. 3. Solve by substitution:
    {x=3yx+y=16\begin{cases} x = 3y \\ x + y = 16 \end{cases}
  4. 4. Solve by substitution:
    {y=4x2x+y=18\begin{cases} y = 4x \\ 2x + y = 18 \end{cases}
  5. 5. Solve by substitution:
    {y=x−23x+y=14\begin{cases} y = x - 2 \\ 3x + y = 14 \end{cases}
  6. 6. Solve by substitution:
    {x=y+5x+2y=11\begin{cases} x = y + 5 \\ x + 2y = 11 \end{cases}
  7. 7. Solve by substitution:
    {y=52x+y=13\begin{cases} y = 5 \\ 2x + y = 13 \end{cases}
  8. 8. Solve by substitution:
    {y=2x+1x+y=10\begin{cases} y = 2x + 1 \\ x + y = 10 \end{cases}

Answer Key

Level 1

  1. 1. (4,8)(4, 8)
  2. 2. (3,6)(3, 6)
  3. 3. (12,4)(12, 4)
  4. 4. (3,12)(3, 12)
  5. 5. (4,2)(4, 2)
  6. 6. (7,2)(7, 2)
  7. 7. (4,5)(4, 5)
  8. 8. (3,7)(3, 7)

Grade 8 Algebra: Solving Systems by Substitution

Name: ______________________Date: ____________Score: ____ / 8

Level 2

Negatives and coefficients

  1. 1. Solve by substitution:
    {y=−2x+33x+y=5\begin{cases} y = -2x + 3 \\ 3x + y = 5 \end{cases}
  2. 2. Solve by substitution:
    {y=x−42x+3y=3\begin{cases} y = x - 4 \\ 2x + 3y = 3 \end{cases}
  3. 3. Solve by substitution:
    {x=2y−13x−y=7\begin{cases} x = 2y - 1 \\ 3x - y = 7 \end{cases}
  4. 4. Solve by substitution:
    {y=3x+24x−y=−5\begin{cases} y = 3x + 2 \\ 4x - y = -5 \end{cases}
  5. 5. Solve by substitution:
    {x=−y+62x−3y=−3\begin{cases} x = -y + 6 \\ 2x - 3y = -3 \end{cases}
  6. 6. Solve by substitution:
    {y=−x−15x+2y=4\begin{cases} y = -x - 1 \\ 5x + 2y = 4 \end{cases}
  7. 7. Solve by substitution:
    {y=2x−3y=−x+6\begin{cases} y = 2x - 3 \\ y = -x + 6 \end{cases}
  8. 8. Solve by substitution:
    {x=4y2x−5y=−6\begin{cases} x = 4y \\ 2x - 5y = -6 \end{cases}

Answer Key

Level 2

  1. 1. (2,−1)(2, -1)
  2. 2. (3,−1)(3, -1)
  3. 3. (3,2)(3, 2)
  4. 4. (−3,−7)(-3, -7)
  5. 5. (3,3)(3, 3)
  6. 6. (2,−3)(2, -3)
  7. 7. (3,3)(3, 3)
  8. 8. (−8,−2)(-8, -2)

Grade 8 Algebra: Solving Systems by Substitution

Name: ______________________Date: ____________Score: ____ / 8

Level 3

Isolate first; special cases

  1. 1. Solve by substitution:
    {x+y=72x−y=2\begin{cases} x + y = 7 \\ 2x - y = 2 \end{cases}
  2. 2. Solve by substitution:
    {x−2y=13x+y=10\begin{cases} x - 2y = 1 \\ 3x + y = 10 \end{cases}
  3. 3. Solve by substitution:
    {2x+y=−14x−3y=13\begin{cases} 2x + y = -1 \\ 4x - 3y = 13 \end{cases}
  4. 4. Solve by substitution:
    {y=2x+54x−2y=6\begin{cases} y = 2x + 5 \\ 4x - 2y = 6 \end{cases}
  5. 5. Solve by substitution:
    {y=3x−16x−2y=2\begin{cases} y = 3x - 1 \\ 6x - 2y = 2 \end{cases}
  6. 6. Solve by substitution:
    {x+3y=42x−y=−6\begin{cases} x + 3y = 4 \\ 2x - y = -6 \end{cases}
  7. 7. Solve by substitution:
    {3x+2y=8x−y=6\begin{cases} 3x + 2y = 8 \\ x - y = 6 \end{cases}
  8. 8. Solve by substitution:
    {y=12x+2x+2y=12\begin{cases} y = \tfrac{1}{2}x + 2 \\ x + 2y = 12 \end{cases}

Answer Key

Level 3

  1. 1. (3,4)(3, 4)
  2. 2. (3,1)(3, 1)
  3. 3. (1,−3)(1, -3)
  4. 4. No solution\text{No solution}
  5. 5. Infinitely many\text{Infinitely many}
  6. 6. (−2,2)(-2, 2)
  7. 7. (4,−2)(4, -2)
  8. 8. (4,4)(4, 4)

Grade 8 Algebra: Solving Systems by Elimination

Name: ______________________Date: ____________Score: ____ / 8

Level 1

Add or subtract directly

  1. 1. Solve by elimination:
    {x+y=10x−y=2\begin{cases} x + y = 10 \\ x - y = 2 \end{cases}
  2. 2. Solve by elimination:
    {x+y=8x−y=4\begin{cases} x + y = 8 \\ x - y = 4 \end{cases}
  3. 3. Solve by elimination:
    {2x+y=11x−y=1\begin{cases} 2x + y = 11 \\ x - y = 1 \end{cases}
  4. 4. Solve by elimination:
    {x+3y=10−x+y=2\begin{cases} x + 3y = 10 \\ -x + y = 2 \end{cases}
  5. 5. Solve by elimination:
    {3x+y=14x+y=6\begin{cases} 3x + y = 14 \\ x + y = 6 \end{cases}
  6. 6. Solve by elimination:
    {2x+5y=162x+y=8\begin{cases} 2x + 5y = 16 \\ 2x + y = 8 \end{cases}
  7. 7. Solve by elimination:
    {x+2y=7−x+3y=8\begin{cases} x + 2y = 7 \\ -x + 3y = 8 \end{cases}
  8. 8. Solve by elimination:
    {4x−y=92x+y=9\begin{cases} 4x - y = 9 \\ 2x + y = 9 \end{cases}

Answer Key

Level 1

  1. 1. (6,4)(6, 4)
  2. 2. (6,2)(6, 2)
  3. 3. (4,3)(4, 3)
  4. 4. (1,3)(1, 3)
  5. 5. (4,2)(4, 2)
  6. 6. (3,2)(3, 2)
  7. 7. (1,3)(1, 3)
  8. 8. (3,3)(3, 3)

Grade 8 Algebra: Solving Systems by Elimination

Name: ______________________Date: ____________Score: ____ / 8

Level 2

Multiply one equation

  1. 1. Solve by elimination:
    {x+2y=53x−y=8\begin{cases} x + 2y = 5 \\ 3x - y = 8 \end{cases}
  2. 2. Solve by elimination:
    {2x+y=7x+3y=11\begin{cases} 2x + y = 7 \\ x + 3y = 11 \end{cases}
  3. 3. Solve by elimination:
    {3x+2y=1x−y=−3\begin{cases} 3x + 2y = 1 \\ x - y = -3 \end{cases}
  4. 4. Solve by elimination:
    {4x+3y=102x−y=0\begin{cases} 4x + 3y = 10 \\ 2x - y = 0 \end{cases}
  5. 5. Solve by elimination:
    {x−4y=−52x+y=8\begin{cases} x - 4y = -5 \\ 2x + y = 8 \end{cases}
  6. 6. Solve by elimination:
    {5x+2y=3x+y=0\begin{cases} 5x + 2y = 3 \\ x + y = 0 \end{cases}
  7. 7. Solve by elimination:
    {3x−2y=11x+4y=−1\begin{cases} 3x - 2y = 11 \\ x + 4y = -1 \end{cases}
  8. 8. Solve by elimination:
    {2x−3y=−8x+y=1\begin{cases} 2x - 3y = -8 \\ x + y = 1 \end{cases}

Answer Key

Level 2

  1. 1. (3,1)(3, 1)
  2. 2. (2,3)(2, 3)
  3. 3. (−1,2)(-1, 2)
  4. 4. (1,2)(1, 2)
  5. 5. (3,2)(3, 2)
  6. 6. (1,−1)(1, -1)
  7. 7. (3,−1)(3, -1)
  8. 8. (−1,2)(-1, 2)

Grade 8 Algebra: Solving Systems by Elimination

Name: ______________________Date: ____________Score: ____ / 8

Level 3

Multiply both; special cases

  1. 1. Solve by elimination:
    {2x+3y=123x+2y=13\begin{cases} 2x + 3y = 12 \\ 3x + 2y = 13 \end{cases}
  2. 2. Solve by elimination:
    {3x+4y=−12x−3y=−12\begin{cases} 3x + 4y = -1 \\ 2x - 3y = -12 \end{cases}
  3. 3. Solve by elimination:
    {5x−2y=43x+5y=21\begin{cases} 5x - 2y = 4 \\ 3x + 5y = 21 \end{cases}
  4. 4. Solve by elimination:
    {4x+3y=26x−5y=22\begin{cases} 4x + 3y = 2 \\ 6x - 5y = 22 \end{cases}
  5. 5. Solve by elimination:
    {2x+4y=6x+2y=5\begin{cases} 2x + 4y = 6 \\ x + 2y = 5 \end{cases}
  6. 6. Solve by elimination:
    {3x−6y=9x−2y=3\begin{cases} 3x - 6y = 9 \\ x - 2y = 3 \end{cases}
  7. 7. Solve by elimination:
    {7x+2y=−13x−4y=19\begin{cases} 7x + 2y = -1 \\ 3x - 4y = 19 \end{cases}
  8. 8. Solve by elimination:
    {12x+y=42x−3y=2\begin{cases} \tfrac{1}{2}x + y = 4 \\ 2x - 3y = 2 \end{cases}

Answer Key

Level 3

  1. 1. (3,2)(3, 2)
  2. 2. (−3,2)(-3, 2)
  3. 3. (2,3)(2, 3)
  4. 4. (2,−2)(2, -2)
  5. 5. No solution\text{No solution}
  6. 6. Infinitely many\text{Infinitely many}
  7. 7. (1,−4)(1, -4)
  8. 8. (4,2)(4, 2)

Grade 8 Algebra: Word Problems: Systems of Equations

Name: ______________________Date: ____________Score: ____ / 8

Level 1

Sums, differences and simple totals

  1. 1. Solve:
    The\text{The}sum\text{sum}of\text{of}two\text{two}numbers\text{numbers}is\text{is}20\text{20}and\text{and}their\text{their}difference\text{difference}is\text{is}6.\text{6.}Find\text{Find}the\text{the}numbers.\text{numbers.}
  2. 2. Solve:
    A\text{A}shelter\text{shelter}has\text{has}12\text{12}cats\text{cats}and\text{and}dogs.\text{dogs.}There\text{There}are\text{are}4\text{4}more\text{more}dogs\text{dogs}than\text{than}cats.\text{cats.}How\text{How}many\text{many}of\text{of}each?\text{each?}
  3. 3. Solve:
    The\text{The}sum\text{sum}of\text{of}two\text{two}numbers\text{numbers}is\text{is}15.\text{15.}One\text{One}number\text{number}is\text{is}twice\text{twice}the\text{the}other.\text{other.}Find\text{Find}the\text{the}numbers.\text{numbers.}
  4. 4. Solve:
    A\text{A}class\text{class}has\text{has}30\text{30}students.\text{students.}There\text{There}are\text{are}6\text{6}more\text{more}girls\text{girls}than\text{than}boys.\text{boys.}How\text{How}many\text{many}of\text{of}each?\text{each?}
  5. 5. Solve:
    Pens\text{Pens}cost\text{cost}2\text{2}dollars\text{dollars}and\text{and}pencils\text{pencils}cost\text{cost}1\text{1}dollar.\text{dollar.}Mia\text{Mia}buys\text{buys}10\text{10}items\text{items}for\text{for}14\text{14}dollars.\text{dollars.}How\text{How}many\text{many}pens\text{pens}and\text{and}pencils?\text{pencils?}
  6. 6. Solve:
    A\text{A}farm\text{farm}has\text{has}chickens\text{chickens}and\text{and}cows\text{cows}with\text{with}20\text{20}heads\text{heads}and\text{and}56\text{56}legs\text{legs}in\text{in}all.\text{all.}How\text{How}many\text{many}of\text{of}each?\text{each?}
  7. 7. Solve:
    A\text{A}rectangle\text{rectangle}has\text{has}a\text{a}perimeter\text{perimeter}of\text{of}30\text{30}cm.\text{cm.}Its\text{Its}length\text{length}is\text{is}5\text{5}cm\text{cm}more\text{more}than\text{than}its\text{its}width.\text{width.}Find\text{Find}the\text{the}length\text{length}and\text{and}width.\text{width.}
  8. 8. Solve:
    The\text{The}sum\text{sum}of\text{of}two\text{two}numbers\text{numbers}is\text{is}25.\text{25.}The\text{The}larger\text{larger}is\text{is}4\text{4}times\text{times}the\text{the}smaller.\text{smaller.}Find\text{Find}the\text{the}numbers.\text{numbers.}

Answer Key

Level 1

  1. 1. 13 and 713\text{ and }7
  2. 2. 8 dogs, 4 cats8\text{ dogs, }4\text{ cats}
  3. 3. 10 and 510\text{ and }5
  4. 4. 18 girls, 12 boys18\text{ girls, }12\text{ boys}
  5. 5. 4 pens, 6 pencils4\text{ pens, }6\text{ pencils}
  6. 6. 12 chickens, 8 cows12\text{ chickens, }8\text{ cows}
  7. 7. 10 cm by 5 cm10\text{ cm by }5\text{ cm}
  8. 8. 20 and 520\text{ and }5

Grade 8 Algebra: Word Problems: Systems of Equations

Name: ______________________Date: ____________Score: ____ / 8

Level 2

Costs, coins and comparing plans

  1. 1. Solve:
    Adult\text{Adult}movie\text{movie}tickets\text{tickets}cost\text{cost}9\text{9}dollars\text{dollars}and\text{and}child\text{child}tickets\text{tickets}cost\text{cost}6\text{6}dollars.\text{dollars.}A\text{A}family\text{family}buys\text{buys}8\text{8}tickets\text{tickets}for\text{for}60\text{60}dollars.\text{dollars.}How\text{How}many\text{many}of\text{of}each?\text{each?}
  2. 2. Solve:
    One\text{One}gym\text{gym}charges\text{charges}20\text{20}dollars\text{dollars}plus\text{plus}5\text{5}dollars\text{dollars}per\text{per}visit.\text{visit.}Another\text{Another}charges\text{charges}9\text{9}dollars\text{dollars}per\text{per}visit.\text{visit.}After\text{After}how\text{how}many\text{many}visits\text{visits}is\text{is}the\text{the}cost\text{cost}the\text{the}same,\text{same,}and\text{and}what\text{what}is\text{is}it?\text{it?}
  3. 3. Solve:
    Leo\text{Leo}has\text{has}15\text{15}dimes\text{dimes}and\text{and}quarters\text{quarters}worth\text{worth}2.25\text{2.25}dollars.\text{dollars.}How\text{How}many\text{many}of\text{of}each\text{each}coin?\text{coin?}
  4. 4. Solve:
    Three\text{Three}coffees\text{coffees}and\text{and}two\text{two}muffins\text{muffins}cost\text{cost}13\text{13}dollars.\text{dollars.}One\text{One}coffee\text{coffee}and\text{and}two\text{two}muffins\text{muffins}cost\text{cost}7\text{7}dollars.\text{dollars.}Find\text{Find}the\text{the}price\text{price}of\text{of}each.\text{each.}
  5. 5. Solve:
    A\text{A}test\text{test}has\text{has}20\text{20}questions\text{questions}worth\text{worth}2\text{2}or\text{or}5\text{5}points\text{points}each,\text{each,}for\text{for}64\text{64}points\text{points}in\text{in}all.\text{all.}How\text{How}many\text{many}of\text{of}each\text{each}type?\text{type?}
  6. 6. Solve:
    One\text{One}taxi\text{taxi}charges\text{charges}3\text{3}dollars\text{dollars}plus\text{plus}2\text{2}dollars\text{dollars}per\text{per}mile.\text{mile.}Another\text{Another}charges\text{charges}6\text{6}dollars\text{dollars}plus\text{plus}1.5\text{1.5}dollars\text{dollars}per\text{per}mile.\text{mile.}For\text{For}how\text{how}many\text{many}miles\text{miles}is\text{is}the\text{the}cost\text{cost}equal,\text{equal,}and\text{and}what\text{what}is\text{is}it?\text{it?}
  7. 7. Solve:
    Two\text{Two}numbers\text{numbers}differ\text{differ}by\text{by}9.\text{9.}Twice\text{Twice}the\text{the}larger\text{larger}plus\text{plus}the\text{the}smaller\text{smaller}is\text{is}33.\text{33.}Find\text{Find}the\text{the}numbers.\text{numbers.}
  8. 8. Solve:
    Two\text{Two}apples\text{apples}and\text{and}three\text{three}bananas\text{bananas}cost\text{cost}4.50\text{4.50}dollars.\text{dollars.}Four\text{Four}apples\text{apples}and\text{and}one\text{one}banana\text{banana}cost\text{cost}4\text{4}dollars.\text{dollars.}Find\text{Find}the\text{the}price\text{price}of\text{of}each.\text{each.}

Answer Key

Level 2

  1. 1. 4 adult, 4 child4\text{ adult, }4\text{ child}
  2. 2. 5 visits, $455\text{ visits, }\$45
  3. 3. 10 dimes, 5 quarters10\text{ dimes, }5\text{ quarters}
  4. 4. coffee $3, muffin $2\text{coffee }\$3,\ \text{muffin }\$2
  5. 5. 12 two-point, 8 five-point12\text{ two-point, }8\text{ five-point}
  6. 6. 6 miles, $156\text{ miles, }\$15
  7. 7. 14 and 514\text{ and }5
  8. 8. apple $0.75, banana $1\text{apple }\$0.75,\ \text{banana }\$1

Grade 8 Algebra: Word Problems: Systems of Equations

Name: ______________________Date: ____________Score: ____ / 8

Level 3

Speed, mixtures, ages and digits

  1. 1. Solve:
    A\text{A}boat\text{boat}goes\text{goes}24\text{24}miles\text{miles}downstream\text{downstream}in\text{in}2\text{2}hours\text{hours}and\text{and}back\text{back}upstream\text{upstream}in\text{in}3\text{3}hours.\text{hours.}Find\text{Find}the\text{the}speed\text{speed}of\text{of}the\text{the}boat\text{boat}in\text{in}still\text{still}water\text{water}and\text{and}of\text{of}the\text{the}current.\text{current.}
  2. 2. Solve:
    How\text{How}many\text{many}liters\text{liters}of\text{of}a\text{a}20\text{20}percent\text{percent}solution\text{solution}and\text{and}a\text{a}40\text{40}percent\text{percent}solution\text{solution}make\text{make}10\text{10}liters\text{liters}of\text{of}a\text{a}28\text{28}percent\text{percent}solution?\text{solution?}
  3. 3. Solve:
    A\text{A}mother\text{mother}is\text{is}3\text{3}times\text{times}as\text{as}old\text{old}as\text{as}her\text{her}son.\text{son.}In\text{In}10\text{10}years\text{years}she\text{she}will\text{will}be\text{be}twice\text{twice}as\text{as}old\text{old}as\text{as}him.\text{him.}Find\text{Find}their\text{their}ages\text{ages}now.\text{now.}
  4. 4. Solve:
    A\text{A}rectangle\text{rectangle}has\text{has}a\text{a}perimeter\text{perimeter}of\text{of}40\text{40}m.m\text{.}Its\text{Its}length\text{length}is\text{is}4\text{4}mm\text{}less\text{less}than\text{than}3\text{3}times\text{times}its\text{its}width.\text{width.}Find\text{Find}the\text{the}length\text{length}and\text{and}width.\text{width.}
  5. 5. Solve:
    A\text{A}plane\text{plane}flies\text{flies}600\text{600}miles\text{miles}with\text{with}the\text{the}wind\text{wind}in\text{in}3\text{3}hours\text{hours}and\text{and}600\text{600}miles\text{miles}against\text{against}the\text{the}wind\text{wind}in\text{in}4\text{4}hours.\text{hours.}Find\text{Find}the\text{the}speed\text{speed}of\text{of}the\text{the}plane\text{plane}and\text{and}of\text{of}the\text{the}wind.\text{wind.}
  6. 6. Solve:
    A\text{A}concert\text{concert}sold\text{sold}500\text{500}tickets\text{tickets}for\text{for}9500\text{9500}dollars.\text{dollars.}Floor\text{Floor}seats\text{seats}cost\text{cost}25\text{25}dollars\text{dollars}and\text{and}balcony\text{balcony}seats\text{seats}cost\text{cost}15\text{15}dollars.\text{dollars.}How\text{How}many\text{many}of\text{of}each\text{each}were\text{were}sold?\text{sold?}
  7. 7. Solve:
    One\text{One}phone\text{phone}plan\text{plan}costs\text{costs}40\text{40}dollars\text{dollars}plus\text{plus}0.10\text{0.10}dollars\text{dollars}per\text{per}text.\text{text.}Another\text{Another}costs\text{costs}25\text{25}dollars\text{dollars}plus\text{plus}0.25\text{0.25}dollars\text{dollars}per\text{per}text.\text{text.}For\text{For}how\text{how}many\text{many}texts\text{texts}are\text{are}they\text{they}equal,\text{equal,}and\text{and}what\text{what}is\text{is}the\text{the}cost?\text{cost?}
  8. 8. Solve:
    The\text{The}digits\text{digits}of\text{of}a\text{a}two-digit\text{two-digit}number\text{number}add\text{add}up\text{up}to\text{to}9.\text{9.}Reversing\text{Reversing}the\text{the}digits\text{digits}makes\text{makes}the\text{the}number\text{number}27\text{27}larger.\text{larger.}Find\text{Find}the\text{the}number.\text{number.}

Answer Key

Level 3

  1. 1. boat 10 mph, current 2 mph\text{boat }10\text{ mph, current }2\text{ mph}
  2. 2. 6 L of 20%, 4 L of 40%6\text{ L of }20\%,\ 4\text{ L of }40\%
  3. 3. son 10, mother 30\text{son }10,\ \text{mother }30
  4. 4. 14 m by 6 m14\text{ m by }6\text{ m}
  5. 5. plane 175 mph, wind 25 mph\text{plane }175\text{ mph, wind }25\text{ mph}
  6. 6. 200 floor, 300 balcony200\text{ floor, }300\text{ balcony}
  7. 7. 100 texts, $50100\text{ texts, }\$50
  8. 8. 3636