Skills · Linear Equations · Systems of Equations

Systems: graphing

Printable practice with an answer key the engine computes, at three levels, in as many versions as you need.

Problem types

• two lines that cross: y = 2x − 1 and y = −x + 5
• no solution (parallel lines): y = 2x + 1 and y = 2x − 3
• infinitely many solutions (same line): y = 2x − 1 and 4x − 2y = 2

Sample Sheet · Level 1

1. y = 2x − 1
   y = x − 2
2. y = x + 1
   y = 3x + 1
3. y = 3x − 4
   y = −x + 4
4. y = −x
   y = −x + 3
5. y = 2x − 4
   y = 3x − 5
6. y = −x − 1
   y = x + 5
7. y = 3x
   y = −x
8. y = x
   y = 3x − 2

Answer key

1. (−1, −3)
2. (0, 1)
3. (2, 2)
4. no solution
5. (1, −2)
6. (−3, 2)
7. (0, 0)
8. (1, 1)

Sample Sheet · Level 3

1. y = x − 5
   x + y = 3
2. y = −2x + 4
   x − y = −1
3. x − y = −2
   y = x − 5
4. y = −3x + 5
   2x + y = 2
5. y = −12x + 1
   2x + y = −2
6. y = −3x − 1
   9x + 3y = −3
7. 2x + y = 0
   x + 3y = 0
8. 2x + y = −3
   y = −3x − 4

Answer key

1. (4, −1)
2. (1, 2)
3. no solution
4. (3, −4)
5. (−2, 2)
6. infinitely many solutions
7. (0, 0)
8. (−1, −1)

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