Solve the system of equations by the addition method.
2x - 4y = 30
- 3x + 3y = - 21

x=−1 and y=−8

Step-by-step explanation:

2x−4y=30;−3x+3y=−21

Step: Solve2x−4y=30for x:

2x−4y+4y=30+4y(Add 4y to both sides)

2x=4y+30

2x

2

=

4y+30

2

(Divide both sides by 2)

x=2y+15

Step: Substitute2y+15forxin−3x+3y=−21:

−3x+3y=−21

−3(2y+15)+3y=−21

−3y−45=−21(Simplify both sides of the equation)

−3y−45+45=−21+45(Add 45 to both sides)

−3y=24

−3y

−3

=

24

−3

(Divide both sides by -3)

y=−8

Step: Substitute−8foryinx=2y+15:

x=2y+15

x=(2)(−8)+15

x=−1(Simplify both sides of the equation)

b. y = 4x - 2

step-by-step explanation:

to find a parallel equation to an equation, make sure both equations have the same slope but different y-intercepts.

y = 4x + 1

4 = slope

1 = y-intercept

y = 4x - 2

4 = slope

-2 = y-intercept

they both have the same slope but different y-intercepts, so, b. is the correct answer.

and to check your work, you can graph both equations. : )