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Checking Solutions of Systems: 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}