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# Graphing Systems of Linear Equations and Inequalities Practice Problems

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Updated on Aug 24, 2011

To review these concepts, go to Graphing Systems of Linear Equations and Inequalities Study Guide.

### Practice

Determine if the following equations are linear equations.

1. 5x + y = 13
2. 6x – 3y = 8
3. y = 12
4. x + y2 = 11
5. 3x + 2xy – 4y = 5
6. y2 + 5x + 6 = 0
7. x + y3 = 11
8. 3x + 2y + 5 = x – y + 7

Graph the systems of equations and state the solution(s).

1. y = 2x + 4

y = 3x + 3

2. y = 2x + 2

3. y = –4x + 1

y = 4x–1

4. 2y + 3x = 12

6y – 2x = 4

5. 5y – 10x = 15

7y + 14x = 21

6. 9x – 3y = 18

4xy = 16

7. –28x + 4y = 32

16x – 16y= –48

8. –9x + 6y= 12

30x – 15y = 15

9. 200y – 400x = –600

75y + 150x = 300

10. –17x – 17y = 17

–19x – 19y = 19

Without graphing the system, determine the number of solutions the system will have.

1. y = 3x – 5

y = 3x + 2

2. x + 3y = 10

2x + 6y = 20

3. 3y – 2x = 6

2y – 3x = 4

4. 2x + 3y = 6

3x – y = 2

5. y + 3 = 3x + 5

3y = 9x

6. 3x + y = 6

3x – y= 6

7. 4x – 3y = 12

–4x + 3y = –12

8. 3x + 3y = 15

–2x – 2y = 8

Solve the systems of inequalities graphically.

1. y > 4

y < x + 2

2. y ≥ 5

x ≤ 2

3. y < x + 2

y < –x + 4

4. x + y > 5

–2x + y > 3

5. x ≥ 0

y ≥ 0

y ≤ –2x + 10

6. y = x + 2

y = –x+ 4

7. 2y – x= 2

3x + y = 8

8. 4y = – 7(x + 4)

4y = x + 4

9. y – x = 5 – x

–4y = 8 – 7x

10. 2y = 6x + 14

4y = x – 16

11. 2x + y = 4

3(y + 9) = 7x

12. y = x + 9

4y = 16 – x

13. 4x – 5y = 5

5y = 20 – x

14. 6y = 9(x – 6)

3(2y + 5x) = –6

15. 15y = 6(3x + 15)

y = 6(1 – x)

16. 3y = 6x + 6

5y = 10(x – 5)

17. 3(2x + 3y) = 63

27y = 9(x – 6)

18. x – 20 = 5y

10y = 8x + 20

19. 3x + 4y = 12

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