Question

Solve the system of equations.
–9x+y=12

2x+4y= −28
(1 poin

Answer 1

To solve the system of equations:

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

We can use the substitution or elimination method. Here, I'll use the substitution method.

First, let's solve Equation 1 for \( y \):

\[
y = 9x + 12
\]

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

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

Now, simplify this equation:

\[
2x + 36x + 48 = -28
\]
\[
38x + 48 = -28
\]

Next, isolate \( x \) by subtracting 48 from both sides:

\[
38x = -28 - 48
\]
\[
38x = -76
\]

Now, divide by 38:

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

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

\[
y = 9(-2) + 12
\]
\[
y = -18 + 12
\]
\[
y = -6
\]

Thus, the solution to the system of equations is:

\[
x = -2, \quad y = -6
\]

Finally, we can write the solution as an ordered pair:

\[
(-2, -6)
\]