Question

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

2x+4y= −28
(1 point)

Answer 1

To solve the system of equations:

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

We can use either substitution or elimination. Let's use substitution.

From equation (1), we can express \(y\) in terms of \(x\):

\[
y = 12 + 9x
\]

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

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

Now, distribute the \(4\):

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

Combine like terms:

\[
38x + 48 = -28
\]

Now, subtract \(48\) from both sides:

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

Now, divide by \(38\):

\[
x = \frac{-76}{38} = \frac{-38}{19} = -2
\]

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

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

Thus, the solution to the system of equations is:

\[
(x, y) = (-2, -6)
\]

To verify, plug \(x = -2\) and \(y = -6\) back into the original equations.

For equation (1):

\[
-9(-2) + (-6) = 18 - 6 = 12 \quad \text{(True)}
\]

For equation (2):

\[
2(-2) + 4(-6) = -4 - 24 = -28 \quad \text{(True)}
\]

Both equations are satisfied, so the solution is confirmed:

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