Question

Kuta Software - Infinite Pre-Algebra

Name
Solving Systems of Equations by Substitution
Date
Solve each system by substitution.
1) y = 7x-10
y=-3
2) y=-8
y=-2x - 12
3) y=6x
y=5x+7
4) y = 9x -9
y=9​

Answer 1

Part 1) The solution of the system is the point (1,-3)

Part 2) The solution of the system is the point (-2,-8)

Part 3) The solution of the system is the point (7,42)

Part 4) The solution of the system is the point (2,9)

Explanation:

Part 1) we have

`y=7x-10` ----> equation A

`y=-3` ----> equation B

Solve the system by substitution

Substitute equation B in equation A

`-3=7x-10`

Solve for x

Adds 10 both sides

`-3+10=7x`

`7=7x`

Divide by 7 both sides

`x=1`

The solution of the system is the point (1,-3)

Part 2) we have

`y=-8` ----> equation A

`y=-2x-12` ----> equation B

Solve the system by substitution

Substitute equation A in equation B

`-8=-2x-12`

Solve for x

Adds 12 both sides

`-8+12=-2x`

`4=-2x`

Divide by -2 both sides

`x=-2`

The solution of the system is the point (-2,-8)

Part 3) we have

`y=6x` ----> equation A

`y=5x+7` ----> equation B

Solve the system by substitution

Substitute equation A in equation B

`6x=5x+7`

Solve for x

Subtract 5x both sides

`6x-5x=7`

`x=7`

Find the value of y

`y=6x` ---->
`y=6(7)=42`

The solution of the system is the point (7,42)

Part 4) we have

`y=9x-9` ----> equation A

`y=9` ----> equation B

Solve the system by substitution

Substitute equation B in equation A

`9=9x-9`

Solve for x

Adds 9 both sides

`9+9=9x`

`18=9x`

Divide by 9 both sides

`x=2`

The solution of the system is the point (2,9)