Question

Solve the following system of equations with the elimination method. Write your answers as an Ordered Pair. If infinitely many solutions exist, enter
(oo). If no solution exists, enter DNE
5y + 5x = 10
11y - 15x = -134

Answer 1

To solve the system of equations using the elimination method, we start with the following equations:

1. \( 5y + 5x = 10 \)
2. \( 11y - 15x = -134 \)

Let's first simplify the first equation:

\[
5y + 5x = 10 \implies y + x = 2 \implies y = 2 - x
\]

Now we can substitute \( y = 2 - x \) into the second equation (Equation 2):

\[
11(2 - x) - 15x = -134
\]

Now, distribute \( 11 \):

\[
22 - 11x - 15x = -134
\]

Combine like terms:

\[
22 - 26x = -134
\]

Now, isolate \( x \):

\[
-26x = -134 - 22
\]
\[
-26x = -156
\]
\[
x = \frac{-156}{-26} = 6
\]

Now that we have \( x = 6 \), we can substitute this back into the equation \( y = 2 - x \) to find \( y \):

\[
y = 2 - 6 = -4
\]

Thus, the solution to the system of equations is:

\[
(x, y) = (6, -4)
\]

This can be written as the ordered pair:

\[
\boxed{(6, -4)}
\]