Question

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

y = –8x + 10
y = 10x − 8

(
,
)

Answer 1

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

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

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

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

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

1. Add \( 8x \) to both sides:
\[
10 = 18x - 8
\]

2. Add \( 8 \) to both sides:
\[
10 + 8 = 18x
\]
\[
18 = 18x
\]

3. Divide both sides by \( 18 \):
\[
x = 1
\]

Now that we have \( x = 1 \), we can substitute this value back into one of the original equations to find \( y \). We can use the first equation:

\[
y = -8(1) + 10
\]
\[
y = -8 + 10
\]
\[
y = 2
\]

Thus, the solution to the system of equations is:

\[
(x, y) = (1, 2)
\]

Therefore, the final answer is:

\[
\boxed{(1, 2)}
\]