Solving Systems of Linear Inequalities Worksheet
Name:
Graph and solve each system of linear inequalities. Use a test point to check your shading.
1. 𝑦 > −2𝑥 − 1
𝑦 ≤ 2𝑥 + 3
2. 𝑦 ≤ −2𝑥 + 3
1
𝑦 >− 𝑥−2
3
5
3. 𝑦 ≥ − 2 𝑥 + 2
1
𝑦 ≤− 𝑥−2
2
4. 𝑥 + 3𝑦 > −6
𝑥 − 𝑦 ≥ −2
5. 𝑥 + 𝑦 ≤ 1
𝑦<2
6. 2𝑥 − 3𝑦 < 9
𝑥+𝑦 >2
7. 𝑥 + 3𝑦 > 9
5𝑥 − 3𝑦 ≥ 9
8. Rondell makes $10 and hour cutting grass and $12 an hour for raking leaves. He cannot work
more than 15 hours per week. Rondell wants to earn at least $120 per week.
a. Write a system of inequalities that represents the total hours Rondell can work and the
amount of money he wants to make in a week. Identify your variables.
b. Graph the inequalities to find out how many hours at each job Rondell needs to work.
9. Solve the system of equations by graphing.
𝑦 = 2𝑥 + 1
1
2
𝑦 = 𝑥+4
10. Solve the system of equations by graphing.
2𝑥 + 4𝑦 = 4
𝑦 − 7 = −2𝑥