Systems of Equations

Use substitution to solve the following system of equations.

  1. y = 2x - 1
    2x + 3y = 5

  2. x + 4y = 5
    2y - x = 7

  3. y + 2 = 4x
    3y + 2x = 1

  4. y = 3x + 7
    2y - 6x = 5

 

Use elimination to solve the following systems.

  1. x + 3y = 5
    - x - 7y = 3

  2. - 2x + y = 1
    4x + 3y = 8

  3. 2x + 3y = 7
    x + 5y = 4

  4. 7x + 6y = 8
    5x + 4y = 6

  5. 5x - 10y = - 15
    - 4x + 8y = 12

 

Solve the following systems by any method.

  1. x = 3y - 2
    3x - 5y = 10

  2. x - 2y = 0
    6x - 13y = 5

  3. 8x + 5y = 2
    3x - 1 = 7y

Answers:   1. (1,1)     2. (-3,2)     3. (1/2,0)     4. No Solution     5. (11,-2)

6. (1/2,2)     7. (23/7,1/7)     8. (2,-1)     9. All ordered pairs that satisfy either equation.

10. (10,4)     11. (-10,-5)     12. (19/71,-2/71)

 

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