Skills · Linear Equations · Systems of Equations

Is the point a solution of the system?

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

Problem types

• a point off both lines: Is (1, 4) a solution of y < 2x + 3 and y > −x + 6?
• a point on a dashed boundary: Is (2, 5) a solution of y > x + 3 and y ≤ 2x + 1?
• a point on a solid boundary: Is (2, 5) a solution of y ≥ x + 3 and y ≤ 2x + 1?
• an inequality written with y on the right: Is (1, 2) a solution of x + 4 > y and y ≥ −x + 1?

Sample Sheet · Level 1

1. Is (3, 0) a solution of y < −3x + 4 and y < −2x + 1?
2. Is (−3, 0) a solution of y < x + 2 and y ≥ −2x − 5?
3. Is (2, −4) a solution of y ≥ −3x and y ≤ x − 2?
4. Is (2, −6) a solution of y > x + 4 and y < −3x + 4?
5. Is (−2, −6) a solution of y < 2x and y < −3x + 1?
6. Is (2, 5) a solution of y ≥ −x + 4 and y ≥ −2x + 5?
7. Is (−2, −6) a solution of y ≤ 2x and y < −2x − 5?
8. Is (−3, −3) a solution of y ≥ −x − 1 and y ≥ −2x + 3?

Answer key

1. no
2. no
3. yes
4. no
5. yes
6. yes
7. yes
8. no

Sample Sheet · Level 3

1. Is (1, 3) a solution of x + 5 ≤ y and y ≥ 3x − 1?
2. Is (−1, −5) a solution of y > x − 5 and y ≤ 2x + 1?
3. Is (3, −1) a solution of y ≥ x − 4 and y > −x + 4?
4. Is (3, 9) a solution of 2x + 4 ≥ y and y ≥ −x + 5?
5. Is (3, −1) a solution of y < 2x − 5 and y ≥ −2x + 2?
6. Is (3, 1) a solution of y < 2x − 2 and y ≤ 3x + 4?
7. Is (0, −1) a solution of y < x + 5 and y > −2x − 1?
8. Is (−3, −11) a solution of y ≥ x + 2 and y ≥ 3x − 2?

Answer key

1. no
2. yes
3. no
4. yes
5. yes
6. yes
7. no
8. no

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