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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. Graphing Systems of Linear Equations and Inequalities
  7. Graphing Systems of Linear Equations and Inequalities
  8. y2 + 5x + 6 = 0
  9. x + y3 = 11
  10. 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. Graphing Systems of Linear Equations and Inequalities

    Graphing Systems of Linear Equations and Inequalities

  7. y = x + 2

    y = –x+ 4

  8. 2y – x= 2

    3x + y = 8

  9. 4y = – 7(x + 4)

    4y = x + 4

  10. y – x = 5 – x

    –4y = 8 – 7x

  11. 2y = 6x + 14

    4y = x – 16

  12. 2x + y = 4

    3(y + 9) = 7x

  13. y = x + 9

    4y = 16 – x

  14. 4x – 5y = 5

    5y = 20 – x

  15. 6y = 9(x – 6)

    3(2y + 5x) = –6

  16. 15y = 6(3x + 15)

    y = 6(1 – x)

  17. 3y = 6x + 6

    5y = 10(x – 5)

  18. 3(2x + 3y) = 63

    27y = 9(x – 6)

  19. x – 20 = 5y

    10y = 8x + 20

  20. 3x + 4y = 12

    Graphing Systems of Linear Equations and Inequalities

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