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Systems of Inequalities: Is the Point a Solution? — Easy Worksheet 2
Grade 9 · Whoobee Name: ____________________ Date: __________
Answer yes or no. A point is a solution only if it makes both inequalities true. Points on a dashed line are not included; points on a solid line are.
How to solve
Substitute the point's x and y into each inequality. If both are true, the point is a solution; it lies where the two shadings overlap. If even one is false, it is not. A point on a dashed line is not included (< or >); a point on a solid line is (≤ or ≥).
Example
The graph shows the system y ≥ 2x - 8 and y ≤ -x + 1. Is the point (-3, 3) a solution of the system? Answer yes or no.
Answer: yes
Not quite. The answer is
💡 Substitute x = 4 and y = 4 into each inequality. First: 2(4) − 3 = 8 − 3 = 5, and 4 ≤ 5 is true. Second: 4 − 1 = 3, and 4 ≥ 3 is true. Both are true, so (4, 4) is where the two shadings overlap: yes.
✓ Correct!
Not quite. The answer is
💡 Substitute x = 4 and y = 4 into each inequality. First: 2(4) − 3 = 8 − 3 = 5, and 4 ≤ 5 is true. Second: 4 − 1 = 3, and 4 ≥ 3 is true. Both are true, so (4, 4) is where the two shadings overlap: yes.
💡 How to solve: Systems of Inequalities: Is the Point a Solution?
Substitute the point's x and y into each inequality. If both are true, the point is a solution; it lies where the two shadings overlap. If even one is false, it is not. A point on a dashed line is not included (< or >); a point on a solid line is (≤ or ≥).
Try a similar one
The graph shows the system y ≥ x - 3 and y ≤ 2x - 5. Is the point (6, 5) a solution of the system? Answer yes or no.
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 Substitute x = 0 and y = −4 into each inequality. First: 0 + 5 = 5, and −4 > 5 is false. Second: −2(0) + 8 = 0 + 8 = 8, and −4 ≤ 8 is true. A solution must make both true, so (0, −4) is not a solution: no.
✓ Correct!
Not quite. The answer is
💡 Substitute x = 0 and y = −4 into each inequality. First: 0 + 5 = 5, and −4 > 5 is false. Second: −2(0) + 8 = 0 + 8 = 8, and −4 ≤ 8 is true. A solution must make both true, so (0, −4) is not a solution: no.
💡 How to solve: Systems of Inequalities: Is the Point a Solution?
Substitute the point's x and y into each inequality. If both are true, the point is a solution; it lies where the two shadings overlap. If even one is false, it is not. A point on a dashed line is not included (< or >); a point on a solid line is (≤ or ≥).
Try a similar one
The graph shows the system y < -x + 6 and y ≥ x. Is the point (-6, 4) a solution of the system? Answer yes or no.
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 Substitute x = 4 and y = 4 into each inequality. First: 2(4) + 1 = 8 + 1 = 9, and 4 ≤ 9 is true. Second: −4 + 4 = 0, and 4 ≥ 0 is true. Both are true, so (4, 4) is where the two shadings overlap: yes.
✓ Correct!
Not quite. The answer is
💡 Substitute x = 4 and y = 4 into each inequality. First: 2(4) + 1 = 8 + 1 = 9, and 4 ≤ 9 is true. Second: −4 + 4 = 0, and 4 ≥ 0 is true. Both are true, so (4, 4) is where the two shadings overlap: yes.
💡 How to solve: Systems of Inequalities: Is the Point a Solution?
Substitute the point's x and y into each inequality. If both are true, the point is a solution; it lies where the two shadings overlap. If even one is false, it is not. A point on a dashed line is not included (< or >); a point on a solid line is (≤ or ≥).
Try a similar one
The graph shows the system y < -2x + 3 and y < -x. Is the point (-2, -3) a solution of the system? Answer yes or no.
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 Substitute x = −2 and y = −6 into each inequality. First: −2 − 3 = −5, and −6 ≥ −5 is false. Second: −2(−2) + 3 = 4 + 3 = 7, and −6 < 7 is true. A solution must make both true, so (−2, −6) is not a solution: no.
✓ Correct!
Not quite. The answer is
💡 Substitute x = −2 and y = −6 into each inequality. First: −2 − 3 = −5, and −6 ≥ −5 is false. Second: −2(−2) + 3 = 4 + 3 = 7, and −6 < 7 is true. A solution must make both true, so (−2, −6) is not a solution: no.
💡 How to solve: Systems of Inequalities: Is the Point a Solution?
Substitute the point's x and y into each inequality. If both are true, the point is a solution; it lies where the two shadings overlap. If even one is false, it is not. A point on a dashed line is not included (< or >); a point on a solid line is (≤ or ≥).
Try a similar one
The graph shows the system y ≥ 2x - 5 and y < -2x + 3. Is the point (-2, 6) a solution of the system? Answer yes or no.
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 Substitute x = −3 and y = −5 into each inequality. First: −3 − 3 = −6, and −5 ≥ −6 is true. Second: −2(−3) + 3 = 6 + 3 = 9, and −5 ≤ 9 is true. Both are true, so (−3, −5) is where the two shadings overlap: yes.
✓ Correct!
Not quite. The answer is
💡 Substitute x = −3 and y = −5 into each inequality. First: −3 − 3 = −6, and −5 ≥ −6 is true. Second: −2(−3) + 3 = 6 + 3 = 9, and −5 ≤ 9 is true. Both are true, so (−3, −5) is where the two shadings overlap: yes.
💡 How to solve: Systems of Inequalities: Is the Point a Solution?
Substitute the point's x and y into each inequality. If both are true, the point is a solution; it lies where the two shadings overlap. If even one is false, it is not. A point on a dashed line is not included (< or >); a point on a solid line is (≤ or ≥).
Try a similar one
The graph shows the system y ≥ 2x + 2 and y < x. Is the point (-4, -5) a solution of the system? Answer yes or no.
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 Substitute x = 6 and y = 5 into each inequality. First: 6 − 3 = 3, and 5 ≥ 3 is true. Second: −6 + 1 = −5, and 5 < −5 is false. A solution must make both true, so (6, 5) is not a solution: no.
✓ Correct!
Not quite. The answer is
💡 Substitute x = 6 and y = 5 into each inequality. First: 6 − 3 = 3, and 5 ≥ 3 is true. Second: −6 + 1 = −5, and 5 < −5 is false. A solution must make both true, so (6, 5) is not a solution: no.
💡 How to solve: Systems of Inequalities: Is the Point a Solution?
Substitute the point's x and y into each inequality. If both are true, the point is a solution; it lies where the two shadings overlap. If even one is false, it is not. A point on a dashed line is not included (< or >); a point on a solid line is (≤ or ≥).
Try a similar one
The graph shows the system y > 2x + 9 and y < -2x - 3. Is the point (-6, 3) a solution of the system? Answer yes or no.
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 Substitute x = 2 and y = 1 into each inequality. First: −2 + 2 = 0, and 1 ≥ 0 is true. Second: 2, and 1 ≤ 2 is true. Both are true, so (2, 1) is where the two shadings overlap: yes.
✓ Correct!
Not quite. The answer is
💡 Substitute x = 2 and y = 1 into each inequality. First: −2 + 2 = 0, and 1 ≥ 0 is true. Second: 2, and 1 ≤ 2 is true. Both are true, so (2, 1) is where the two shadings overlap: yes.
💡 How to solve: Systems of Inequalities: Is the Point a Solution?
Substitute the point's x and y into each inequality. If both are true, the point is a solution; it lies where the two shadings overlap. If even one is false, it is not. A point on a dashed line is not included (< or >); a point on a solid line is (≤ or ≥).
Try a similar one
The graph shows the system y > 2x + 4 and y < -2x - 8. Is the point (-6, 0) a solution of the system? Answer yes or no.
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 Substitute x = −4 and y = 1 into each inequality. First: −4 − 3 = −7, and 1 < −7 is false. Second: −(−4) + 3 = 4 + 3 = 7, and 1 < 7 is true. A solution must make both true, so (−4, 1) is not a solution: no.
✓ Correct!
Not quite. The answer is
💡 Substitute x = −4 and y = 1 into each inequality. First: −4 − 3 = −7, and 1 < −7 is false. Second: −(−4) + 3 = 4 + 3 = 7, and 1 < 7 is true. A solution must make both true, so (−4, 1) is not a solution: no.
💡 How to solve: Systems of Inequalities: Is the Point a Solution?
Substitute the point's x and y into each inequality. If both are true, the point is a solution; it lies where the two shadings overlap. If even one is false, it is not. A point on a dashed line is not included (< or >); a point on a solid line is (≤ or ≥).
Try a similar one
The graph shows the system y ≤ -x - 1 and y < 2x + 2. Is the point (1, -6) a solution of the system? Answer yes or no.
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
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Systems of Inequalities: Is the Point a Solution? — Easy Worksheet 2
Answer yes or no. A point is a solution only if it makes both inequalities true. Points on a dashed line are not included; points on a solid line are.