Question

Solve using substitution.

y = –6x − 3
y = –4x − 5

(
,
)

Answer 1

To solve the system of equations using substitution, we will substitute the expression for \( y \) from one equation into the other.

We have the two equations:
1. \( y = -6x - 3 \)
2. \( y = -4x - 5 \)

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

\[
-6x - 3 = -4x - 5
\]

Next, we'll solve for \( x \). First, let’s get all the \( x \) terms on one side by adding \( 6x \) to both sides:

\[
-3 = 2x - 5
\]

Now add \( 5 \) to both sides:

\[
-3 + 5 = 2x
\]

This simplifies to:

\[
2 = 2x
\]

Now, divide both sides by \( 2 \):

\[
x = 1
\]

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

\[
y = -6(1) - 3
\]
\[
y = -6 - 3
\]
\[
y = -9
\]

So, the solution to the system of equations is:

\[
(x, y) = (1, -9)
\]

Thus, the final answer is:

\[
(1, -9)
\]