Kuta Software - Infinite Algebra 2
Name___________________________________
Systems of Inequalities
Date________________ Period____
Sketch the solution to each system of inequalities.
1) y > 4 x − 3
y ≥ −2 x + 3
−5
−4
−3
−2
2) y ≥ −5 x + 3
y > −2
5
5
4
4
3
3
2
2
1
1
−1 0
−1
1
2
3
4
5
−4
−3
−2
−4
−3
−2
−1 0
−1
−2
−2
−3
−3
−4
−4
−5
−5
3) y < 3
y ≤ −x + 1
−5
−5
1
2
3
4
5
1
2
3
4
5
4) y ≥ x − 3
y ≥ −x − 1
5
5
4
4
3
3
2
2
1
1
−1 0
−1
1
2
3
4
5
−5
−4
−3
−2
−1 0
−1
−2
−2
−3
−3
−4
−4
−5
−5
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Worksheet by Kuta Software LLC
5) x ≤ −3
5 x + 3 y ≥ −9
−5
−4
−3
−2
6) 4 x − 3 y < 9
x + 3y > 6
5
5
4
4
3
3
2
2
1
1
−1 0
−1
1
2
3
4
5
−4
−3
−2
−4
−3
−2
−1 0
−1
−2
−2
−3
−3
−4
−4
−5
−5
7) x + y > 2
2x − y > 1
−5
−5
1
2
3
4
5
1
2
3
4
5
8) x + y ≥ 2
4 x + y ≥ −1
5
5
4
4
3
3
2
2
1
1
−1 0
−1
1
2
3
4
5
−5
−4
−3
−2
−1 0
−1
−2
−2
−3
−3
−4
−4
−5
−5
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Worksheet by Kuta Software LLC
9) 4 x + 3 y > −6
x − 3 y ≤ −9
−5
−4
−3
−2
10) y < −2
x+ y≥1
5
5
4
4
3
3
2
2
1
1
−1 0
−1
1
2
3
4
5
−4
−3
−2
−4
−3
−2
−1 0
−1
−2
−2
−3
−3
−4
−4
−5
−5
11) 3 x + y ≥ −3
x + 2y ≤ 4
−5
−5
1
2
3
4
5
1
2
3
4
5
12) x + y ≥ −3
x+ y≤3
5
5
4
4
3
3
2
2
1
1
−1 0
−1
1
2
3
4
5
−5
−4
−3
−2
−1 0
−1
−2
−2
−3
−3
−4
−4
−5
−5
Critical thinking questions:
13) State one solution to the system
y < 2x − 1
y ≥ 10 − x
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14) Write a system of inequalities whose solution
is the set of all points in quadrant I not including
the axes.
-3-
Worksheet by Kuta Software LLC
Kuta Software - Infinite Algebra 2
Name___________________________________
Systems of Inequalities
Date________________ Period____
Sketch the solution to each system of inequalities.
1) y > 4 x − 3
y ≥ −2 x + 3
−5
−4
−3
−2
2) y ≥ −5 x + 3
y > −2
5
5
4
4
3
3
2
2
1
1
−1 0
−1
1
2
3
4
5
−4
−3
−2
−4
−3
−2
−1 0
−1
−2
−2
−3
−3
−4
−4
−5
−5
3) y < 3
y ≤ −x + 1
−5
−5
1
2
3
4
5
1
2
3
4
5
4) y ≥ x − 3
y ≥ −x − 1
5
5
4
4
3
3
2
2
1
1
−1 0
−1
1
2
3
4
5
−5
−4
−3
−2
−1 0
−1
−2
−2
−3
−3
−4
−4
−5
−5
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-1-
Worksheet by Kuta Software LLC
5) x ≤ −3
5 x + 3 y ≥ −9
−5
−4
−3
−2
6) 4 x − 3 y < 9
x + 3y > 6
5
5
4
4
3
3
2
2
1
1
−1 0
−1
1
2
3
4
5
−4
−3
−2
−4
−3
−2
−1 0
−1
−2
−2
−3
−3
−4
−4
−5
−5
7) x + y > 2
2x − y > 1
−5
−5
1
2
3
4
5
1
2
3
4
5
8) x + y ≥ 2
4 x + y ≥ −1
5
5
4
4
3
3
2
2
1
1
−1 0
−1
1
2
3
4
5
−5
−4
−3
−2
−1 0
−1
−2
−2
−3
−3
−4
−4
−5
−5
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-2-
Worksheet by Kuta Software LLC
9) 4 x + 3 y > −6
x − 3 y ≤ −9
−5
−4
−3
−2
10) y < −2
x+ y≥1
5
5
4
4
3
3
2
2
1
1
−1 0
−1
1
2
3
4
5
−4
−3
−2
−4
−3
−2
−1 0
−1
−2
−2
−3
−3
−4
−4
−5
−5
11) 3 x + y ≥ −3
x + 2y ≤ 4
−5
−5
1
2
3
4
5
1
2
3
4
5
12) x + y ≥ −3
x+ y≤3
5
5
4
4
3
3
2
2
1
1
−1 0
−1
1
2
3
4
5
−5
−4
−3
−2
−1 0
−1
−2
−2
−3
−3
−4
−4
−5
−5
Critical thinking questions:
13) State one solution to the system
y < 2x − 1
y ≥ 10 − x
14) Write a system of inequalities whose solution
is the set of all points in quadrant I not including
the axes.
Many solutions. Ex: (10, 10) or (5, 8)
x > 0, y > 0
Create your own worksheets like this one with Infinite Algebra 2. Free trial available at KutaSoftware.com
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Worksheet by Kuta Software LLC