Question

Solve the system of linear equations

y = 7x + 15
y = −2x − 3

Group of answer choices

(-2,1)

(-2,-1)

(-5,5)

(5,-2)

Answer 1

To solve the system of equations:

1. \( y = 7x + 15 \)
2. \( y = -2x - 3 \)

We can set the two equations equal to each other since both are equal to \( y \):

\[
7x + 15 = -2x - 3
\]

Now, combine like terms:

\[
7x + 2x = -3 - 15
\]

This simplifies to:

\[
9x = -18
\]

Now, divide both sides by 9:

\[
x = -2
\]

Now that we have \( x = -2 \), we can substitute it back into either of the original equations to find \( y \). We'll use the second equation, \( y = -2x - 3 \):

\[
y = -2(-2) - 3
\]
\[
y = 4 - 3
\]
\[
y = 1
\]

So the solution to the system of equations is \( (x, y) = (-2, 1) \).

Thus, the answer is:

\[
\boxed{(-2, 1)}
\]