Question

Given the system of equations presented here:

4x + y = 4
2x + 6y = 24
Which action creates an equivalent system that will eliminate one variable when they are combined?

A.Multiply the first equation by -4 to get -16x - 4y = -16.

B.Multiply the second equation by -4 to get - 8x - 24y = -96.

C.Multiply the first equation by -2 to get -8x - 2y = -8.

D.Multiply the second equation by -2 to get - 4x - 12y = -48.​

Answer 1

D.Multiply the second equation by -2

to get - 4x - 12y = -48.​

Explanation:

`\left\{\begin{array}{ccc}4x+y=4\\2x+6y=24&\text{multiply both sides by (-2)}\end{array}\right\\\\\underline{+\left\{\begin{array}{ccc}4x+y=4\\-4x-12y=-48\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad\qquad11y=-44\qquad\text{divide both sides by 11}\\.\qquad\qquad y=-4\\\\\text{put the value of y to the first equation:}\\\\4x+(-4)=4\\4x-4=4\qquad\text{add 4 to both sides}\\4x=8\qquad\text{divide both sides by 4}\\x=2`

Answer 2

Answer:

Multiply the second equation by -2 to get
`- 4x - 12y = -48`

Explanation:

`4x + y = 4`

`2x + 6y = 24`

To eliminate one variable the coefficient of a variable should be same with opposite sign.

LEts check with each option

Multiply the first equation by -4 to get
`-16x - 4y = -16`

the coefficient of x or y are not same when we compare with second equation

Multiply the second equation by -4 to get
`- 8x - 24y = -96`

the coefficient of x or y are not same when we compare with first equation

Multiply the first equation by -2 to get
`-8x - 2y = -8`

the coefficient of x or y are not same when we compare with second equation

Multiply the second equation by -2 to get
`- 4x - 12y = -48`

The coefficient of x terms are same with different sign when compare with first equation

So when we add first and second equation , the x will get eliminated.