Question

Given the following system of equations:

2x + 6y = 12
4x + 3y = 15

Which action creates an equivalent system that will eliminate one variable when they are combined?

Multiply the second equation by −2 to get −8x − 6y = −30.
Multiply the first equation by 2 to get 4x + 12y = 24.
Multiply the second equation by −4 to get −16x − 12y = −60.
Multiply the first equation by −4 to get −8x − 24y = −48.

Answer 1

Answer:

Multiply the second equation by −2 to get −8x − 6y = −30.

Step-by-step explanation:

we have

2x+6y=122x+6y=12 ----> first equation

4x+3y=154x+3y=15 ----> second equation

Solve by elimination

Multiply the second equation by -2 both sides

-2(4x+3y)=-2(15)−2(4x+3y)=−2(15)

-8x-6y=-30−8x−6y=−30 ---> equivalent second equation

Adds first equation and the equivalent second equation

\begin{gathered}2x+6y=12\\-8x-6y=-30\\------\\2x-8x=12-30\\-6x=-18\\x=3\end{gathered}2x+6y=12−8x−6y=−30−−−−−−2x−8x=12−30−6x=−18x=3