To solve the system of equations and eliminate the x variables, we need to ensure that the coefficients of x in both equations are equal in magnitude but opposite in sign.
Here are the given equations:
1) [tex]\(2x - 6y = 20\)[/tex]
2) [tex]\(2x + 5y = -11\)[/tex]
To eliminate the [tex]\(x\)[/tex] variables, we need to add or subtract the equations in such a way that the x terms cancel each other out.
First, let's consider multiplying the top equation by different possible values to see which one facilitates the elimination of [tex]\(x\)[/tex]:
1. Multiplying by -1:
[tex]\[
-1 \cdot (2x - 6y) = -1 \cdot 20 \implies -2x + 6y = -20
\][/tex]
Now, we can add this new equation to the second equation:
[tex]\[
(-2x + 6y) + (2x + 5y) = -20 + (-11) \implies 11y = -31
\][/tex]
This simplifies to:
[tex]\[
11y = -31
\][/tex]
So, multiplying the top equation by -1 is the correct approach. It makes the coefficients of [tex]\(x\)[/tex] equal in magnitude and opposite in sign, allowing the [tex]\(x\)[/tex] terms to cancel out when the equations are added together.
Therefore, the correct answer is: Multiply by [tex]\(-1\)[/tex].
