Question

Solve using substitution.

y = –4x − 6
y = –3x − 3

Answer 1

To solve the system of equations using substitution, we'll follow these steps:

1. We have the two equations:
\[
y = -4x - 6 \quad \text{(1)}
\]
\[
y = -3x - 3 \quad \text{(2)}
\]

2. Since both equations are equal to \(y\), we can set them equal to each other:
\[
-4x - 6 = -3x - 3
\]

3. Now, we will solve for \(x\):
- First, add \(4x\) to both sides:
\[
-6 = x - 3
\]
- Next, add \(3\) to both sides:
\[
-6 + 3 = x
\]
\[
-3 = x
\]

4. Now that we have \(x = -3\), we can substitute this value back into either original equation to find \(y\). We'll use equation (1):
\[
y = -4(-3) - 6
\]
\[
y = 12 - 6
\]
\[
y = 6
\]

5. The solution to the system of equations is:
\[
(x, y) = (-3, 6)
\]

Thus, the point of intersection and the solution to the system of equations is:
\[
\boxed{(-3, 6)}
\]