Skills · Linear Equations · Systems of Equations

Graphing a system of inequalities

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

Problem types

• two boundaries that cross: y < 2x + 1 and y ≥ −x + 4
• no solution (parallel lines shaded apart): y > x + 3 and y < x − 1

Sample Sheet · Level 1

1. y ≤ −x
   y < −2x
2. y < −x + 1
   y < −3x + 5
3. y ≥ −x − 2
   y > x − 4
4. y ≤ x + 3
   y < −2x + 3
5. y < −3x − 5
   y ≤ −2x − 4
6. y ≥ −x + 2
   y < x
7. y < 3x + 1
   y < −2x + 1
8. y ≤ 2x − 1
   y ≤ x − 2

Answer key

1. (−1, 0) is a solution
2. (0, 0) is a solution
3. (0, 0) is a solution
4. (0, 0) is a solution
5. (−2, −1) is a solution
6. (2, 1) is a solution
7. (0, 0) is a solution
8. (1, −2) is a solution

Sample Sheet · Level 3

1. y > −x + 1
   y > x + 3
2. y ≤ −12x − 4
   y ≥ 2x + 1
3. y < x + 2
   y ≥ x + 5
4. y ≤ 2
   y ≤ 13x + 3
5. y ≥ 1
   y ≥ −2x + 1
6. y > x
   y < 3x
7. y ≤ x + 3
   y < 3x + 5
8. y ≤ 2
   y < 12x + 2

Answer key

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

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