Question

Solve using elimination.

–4x + 9y = –13
–x − 2y = 18

Answer 1

To solve the system of equations using the elimination method, we start with the given equations:

1. \(-4x + 9y = -13\) (Equation 1)
2. \(-x - 2y = 18\) (Equation 2)

First, we want to eliminate one of the variables. Let's eliminate \(x\). To do this, we can multiply Equation 2 by 4 so that the coefficients of \(x\) in both equations are the same:

\[
4(-x - 2y) = 4(18)
\]
This simplifies to:
\[
-4x - 8y = 72 \quad \text{(Equation 3)}
\]

Now we have the modified Equation 3 and Equation 1:

1. \(-4x + 9y = -13\) (Equation 1)
2. \(-4x - 8y = 72\) (Equation 3)

Next, we can subtract Equation 3 from Equation 1 to eliminate \(x\):

\[
(-4x + 9y) - (-4x - 8y) = -13 - 72
\]

This simplifies to:
\[
9y + 8y = -13 - 72
\]

Combining like terms gives:
\[
17y = -85
\]

Now, we divide both sides by 17 to solve for \(y\):
\[
y = -5
\]

Now that we have \(y\), we can substitute this value back into either original equation to solve for \(x\). We will use Equation 2:

\[
-x - 2(-5) = 18
\]
This simplifies to:
\[
-x + 10 = 18
\]

Subtracting 10 from both sides results in:
\[
-x = 8
\]

Multiplying both sides by -1 gives us:
\[
x = -8
\]

Thus, the solution to the system of equations is:
\[
\boxed{(-8, -5)}
\]