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Solving Systems by Graphing: Classroom Packet

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}