Question

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

y = 4x + 3
y = x − 6

Answer 1

To solve the system of equations using substitution, we start with the two equations provided:

1. \( y = 4x + 3 \) (Equation 1)
2. \( y = x - 6 \) (Equation 2)

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

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

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

1. Subtract \( x \) from both sides:
\[
4x - x + 3 = -6
\]
\[
3x + 3 = -6
\]

2. Subtract 3 from both sides:
\[
3x = -6 - 3
\]
\[
3x = -9
\]

3. Divide both sides by 3:
\[
x = -3
\]

Now that we have the value of \( x \), we can substitute it back into either of the original equations to find \( y \). We'll use Equation 2:

\[
y = x - 6
\]

Substituting \( x = -3 \):

\[
y = -3 - 6
\]
\[
y = -9
\]

Thus, the solution to the system of equations is:

\[
(x, y) = (-3, -9)
\]

In conclusion, the solution is:

\[
\boxed{(-3, -9)}
\]