To determine which step to perform on the system of equations so that both equations have equal [tex]\(x\)[/tex]-coefficients, follow these steps:
Given:
[tex]\[
\begin{array}{l}
4x + 2y = 4 \\
8x - y = 18
\end{array}
\][/tex]
1. Identify the [tex]\(x\)[/tex]-coefficients in both equations:
- The [tex]\(x\)[/tex]-coefficient in the first equation is [tex]\(4\)[/tex].
- The [tex]\(x\)[/tex]-coefficient in the second equation is [tex]\(8\)[/tex].
2. To make the [tex]\(x\)[/tex]-coefficients equal in both equations, we need to adjust the coefficient [tex]\(4\)[/tex] in the first equation to match the coefficient [tex]\(8\)[/tex] in the second equation.
3. To do this, determine the factor by which you need to multiply the coefficient [tex]\(4\)[/tex] so that it becomes [tex]\(8\)[/tex]. The factor is:
[tex]\[\frac{8}{4} = 2\][/tex]
4. Therefore, we need to multiply both sides of the first equation by [tex]\(2\)[/tex]:
[tex]\[2 \times (4x + 2y) = 2 \times 4\][/tex]
Simplifying, we get:
[tex]\[8x + 4y = 8\][/tex]
Now the new system of equations is:
[tex]\[
\begin{array}{l}
8x + 4y = 8 \\
8x - y = 18
\end{array}
\][/tex]
As we can see, the [tex]\(x\)[/tex]-coefficients in both equations are now equal ([tex]\(8\)[/tex]).
The correct step to perform is to multiply both sides of the top equation by [tex]\(2\)[/tex]. Therefore, the correct option is:
D. Multiply both sides of the top equation by 2
