Question

GG.8 Solve a system of equations using substitution
J8X
Solve using substitution.

y = –x + 8
y = –10x − 10

(
,
)

Answer 1

To solve the system of equations using substitution, we have the following equations:

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

Since both equations are equal to \( y \), we can set them equal to each other:

\[
-x + 8 = -10x - 10
\]

Now, let's solve for \( x \):

1. Add \( 10x \) to both sides:

\[
-x + 10x + 8 = -10
\]

This simplifies to:

\[
9x + 8 = -10
\]

2. Subtract 8 from both sides:

\[
9x = -10 - 8
\]

This simplifies to:

\[
9x = -18
\]

3. Divide both sides by 9:

\[
x = -2
\]

Now, we will substitute \( x = -2 \) back into one of the original equations to find \( y \). Let's use the first equation \( y = -x + 8 \):

\[
y = -(-2) + 8
\]

This simplifies to:

\[
y = 2 + 8 = 10
\]

Thus, the solution to the system of equations is:

\[
(x, y) = (-2, 10)
\]

So the final answer is:

\[
\boxed{(-2, 10)}
\]