Question

Solve the system of equations.
–9x+y=12
2x+4y= −28 (1 point)
(, )

Answer 1

To solve the system of equations:

1. \(-9x + y = 12\) (Equation 1)
2. \(2x + 4y = -28\) (Equation 2)

Let's start by expressing \(y\) in terms of \(x\) using Equation 1:

\[
y = 9x + 12
\]

Now, we can substitute this expression for \(y\) into Equation 2:

\[
2x + 4(9x + 12) = -28
\]

Expanding the equation:

\[
2x + 36x + 48 = -28
\]

Combine like terms:

\[
38x + 48 = -28
\]

Now, subtract 48 from both sides:

\[
38x = -28 - 48
\]

\[
38x = -76
\]

Now, divide by 38:

\[
x = \frac{-76}{38} = -2
\]

Now, substitute back to find \(y\):

\[
y = 9(-2) + 12
\]

\[
y = -18 + 12 = -6
\]

Thus, the solution to the system of equations is:

\[
\boxed{(-2, -6)}
\]