Question

What is the solution to the system of equations?

-2x + y = -5
3x – 2y = 12
Responses

A (3, 1)(3, 1)

B (6, 3)(6, 3)

C (-2, -9)(-2, -9)

D (-2, -1)(-2, -1)

E no solution

Answer 1

To solve the system of equations:

1. **Equation 1:** \(-2x + y = -5\)
2. **Equation 2:** \(3x - 2y = 12\)

Let's solve for \(y\) in the first equation in terms of \(x\):

\[
y = 2x - 5
\]

Now, we can substitute this expression for \(y\) into the second equation:

\[
3x - 2(2x - 5) = 12
\]

Expanding the equation:

\[
3x - 4x + 10 = 12
\]

Combine like terms:

\[
-x + 10 = 12
\]

Now, isolate \(x\):

\[
-x = 12 - 10
\]
\[
-x = 2
\]
\[
x = -2
\]

Now that we have \(x\), we will substitute it back into the equation we derived for \(y\):

\[
y = 2(-2) - 5
\]
\[
y = -4 - 5
\]
\[
y = -9
\]

Thus, the solution to the system of equations is:

\[
(x, y) = (-2, -9)
\]

The correct answer is:

C \((-2, -9)\)