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solve each system by substitution.
y=3x-5
y=-6x-5
????

y=8x-9
y=-8x+7
???


-x+6y=21
y=-5x+12
?????

Answer :

Solution (1):

Given:

  • y = 3x - 5
  • y = -6x - 5

Multiplying y = 3x - 5 by 2:

  • => 2(y = 3x - 5)

               y = -6x - 5

  • => 2y = 6x - 10

               y = -6x - 5

Adding both equations:

  • => 3y = -15

Dividing 3 both sides:

  • => y = -5

Substitute the value of y into any equation.

  • y = -6x - 5
  • => -5 = -6x - 5
  • => 0 = -6x

Divide -6 both sides.

  • => x = 0/-6 = 0

Solution (2):

Given:

  • y = 8x - 9
  • y = -8x + 7

Add both the equations.

  • y = 8x - 9

        y = -8x + 7

  • 2y = -2

Divide 2 both sides.

  • 2y = -2
  • => 2y/2 = -2/2
  • => y = -1

Substitute the value of y into any equation.

  • y = 8x - 9
  • => -1 = 8x - 9

Add 9 both sides.

  • => -1 + 9 = 8x - 9 + 9
  • => 8 = 8x

Divide 8 both sides.

  • => 8/8 = 8x/8
  • => x = 1

Solution (3):

Given:

  • -x + 6y = 21
  • y = -5x + 12

Reorganize the first equation.

  • -x + 6y = 21
  • => 6y = x + 21

Multiply the first equation by 5.

  • 5(6y = x + 21)

          y = -5x + 12

  • 30y = 5x + 105

          y = -5x + 12

Add both the equations.

  • 31y = 117

Divide 31 both sides.

  • 31y = 117
  • => 31y/31 = 117/31
  • => y = 117/31

Substitute the value of y into any equation.

  • -x + 6y = 21
  • => -x + 6(117/31) = 21
  • => -x + 702/31 = 651/31

Subtract 702/31 both sides.

  • => -x = 651/31 - 702/31
  • => -x = -51/31
  • => x = 51/31

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