Question

Solve each system by substitution.

y=3x-5
y=-6x-5
????

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


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

Answer 1

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