Question

Solve using elimination.

–8x − 6y = –8
10x + 6y = –2

(
,
)

Answer 1

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

1) \(-8x - 6y = -8\)
2) \(10x + 6y = -2\)

Let's add the two equations together to eliminate \(y\):

\[
(-8x - 6y) + (10x + 6y) = -8 + (-2)
\]

Combining the left side:

\[
(-8x + 10x) + (-6y + 6y) = -10
\]

This simplifies to:

\[
2x = -10
\]

Now, solve for \(x\):

\[
x = \frac{-10}{2} = -5
\]

Now that we have \(x\), we can substitute it back into one of the original equations to solve for \(y\). We can use the first equation:

\[
-8(-5) - 6y = -8
\]

This simplifies to:

\[
40 - 6y = -8
\]

Now, isolate \(y\):

\[
-6y = -8 - 40
\]
\[
-6y = -48
\]
\[
y = \frac{-48}{-6} = 8
\]

Thus, we have \(x = -5\) and \(y = 8\).

The solution to the system of equations is:

\[
\boxed{(-5, 8)}
\]