Question

Solve the system of equations using substitution.

y=2x+2


y=3x+6


(4 points)
(
,
)

Answer 1

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

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

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

\[
2x + 2 = 3x + 6
\]

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

1. Subtract \( 2x \) from both sides:
\[
2 = x + 6
\]

2. Subtract \( 6 \) from both sides:
\[
2 - 6 = x
\]
\[
-4 = x
\]

Now that we have \( x = -4 \), we can substitute this value back into one of the original equations to find \( y \). Let's use the first equation:

\[
y = 2(-4) + 2
\]
\[
y = -8 + 2
\]
\[
y = -6
\]

Thus, the solution to the system of equations is:
\[
(x, y) = (-4, -6)
\]

In coordinate form:
\[
\boxed{(-4, -6)}
\]