Question

Solve using elimination.

–8x − 9y = –9
x + 3y = 18

Answer 1

To solve the system of equations using the elimination method, we have the following equations:

1. \(-8x - 9y = -9\)
2. \(x + 3y = 18\)

First, we can manipulate the equations for easier elimination. We will multiply the second equation by 8 to match the coefficient of \(x\) in the first equation:

\[
8(x + 3y) = 8(18)
\]

This simplifies to:

\[
8x + 24y = 144
\]

Now, we rewrite our system of equations:

1. \(-8x - 9y = -9\)
2. \(8x + 24y = 144\)

Next, we can add these two equations together to eliminate \(x\):

\[
(-8x - 9y) + (8x + 24y) = -9 + 144
\]

This simplifies to:

\[
0x + 15y = 135
\]

Now, we can solve for \(y\):

\[
15y = 135
\]

Divide both sides by 15:

\[
y = 9
\]

Now that we have \(y\), we can substitute it back into one of the original equations to solve for \(x\). We'll use the second equation:

\[
x + 3y = 18
\]

Substituting \(y = 9\):

\[
x + 3(9) = 18
\]
\[
x + 27 = 18
\]

Subtract 27 from both sides:

\[
x = 18 - 27
\]
\[
x = -9
\]

Now we have the solution:

\[
\boxed{(-9, 9)}
\]

This means \(x = -9\) and \(y = 9\).