Question

Solve using substitution.

y = –6x + 9
y = –4x + 5

(
,
)

Answer 1

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

1. \( y = -6x + 9 \)
2. \( y = -4x + 5 \)

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

\[
-6x + 9 = -4x + 5
\]

Next, we will solve for \( x \):

1. Move \( -4x \) to the left side:

\[
-6x + 4x + 9 = 5
\]

This simplifies to:

\[
-2x + 9 = 5
\]

2. Now, subtract 9 from both sides:

\[
-2x = 5 - 9
\]

\[
-2x = -4
\]

3. Divide by -2:

\[
x = \frac{-4}{-2} = 2
\]

Now that we have the value of \( x \), we substitute it back into one of the original equations to find \( y \). We'll use the first equation:

\[
y = -6(2) + 9
\]

Calculating this gives:

\[
y = -12 + 9 = -3
\]

Thus, the solution to the system of equations is:

\[
(x, y) = (2, -3)
\]

So, the final answer is:

\[
\boxed{(2, -3)}
\]