Question

when solving the following system of equations using the elimination method, what would be the appropriate first step?A) multiply the bottom equation by 2B) multiply the top equation by 4 C) subtract the system D) add the system

Answer 1

A) multiply the bottom equation by 2

Step-by-step explanation:

Our goal in using the elimination method is to eliminate one variable so that we can solve for another independently.

Therefore, the first step would be to multiply the bottom equation by 2 so that the term with x becomes -4x so that it can cancel when the bottom equation Is added to the equation at the top.

Multiplying the bottom equation by -2 gives

`\begin{gathered} 2(-2x+5y=25) \\ -4x+10y=50 \end{gathered}`

Now, our system becomes

`\begin{gathered} 4x+7y=28 \\ -4x+10y=50 \end{gathered}`

adding the two equations gives

`\begin{gathered} 4x+7y=28 \\ -4x+10y=50 \\ -------------- \\ 17y=78 \end{gathered}`

we can now solve for y and then use its value to find the value of x.

Therefore, the correct first step in solving the equations is to multiply the bottom equation by 2.