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

Answer:

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)

Step-by-step 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)