Question

Solve using elimination.

–10x − 8y = 4
–x − 2y = –8

(
,
)

Answer 1

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

1) \( -10x - 8y = 4 \)
2) \( -x - 2y = -8 \)

First, we can manipulate the second equation to align it with the first. We can multiply the second equation by 10 to eliminate \( x \):

\[
10(-x - 2y) = 10(-8)
\]
This gives us:

\[
-10x - 20y = -80
\]

Now our system of equations looks like this:

1) \( -10x - 8y = 4 \)
2) \( -10x - 20y = -80 \)

Next, we subtract the first equation from the second:

\[
(-10x - 20y) - (-10x - 8y) = -80 - 4
\]

This simplifies to:

\[
-20y + 8y = -84
\]
\[
-12y = -84
\]

Now, divide both sides by -12:

\[
y = \frac{-84}{-12} = 7
\]

Now that we have \( y \), we can substitute \( y = 7 \) back into the second equation to find \( x \):

\[
-x - 2(7) = -8
\]
\[
-x - 14 = -8
\]
Adding 14 to both sides gives:

\[
-x = 6
\]

Thus, dividing by -1:

\[
x = -6
\]

Now we have the solution:

\[
(x, y) = (-6, 7)
\]

So the final answer is:

\[
\boxed{(-6, 7)}
\]