Question

Solve using elimination.

–5x − 8y = 15
–5x − 4y = –5

Answer 1

To solve the system of equations using elimination, we'll start with the two provided equations:

1) \(-5x - 8y = 15\) (Equation 1)
2) \(-5x - 4y = -5\) (Equation 2)

We notice that both equations have the same coefficient for \(x\) (-5). We can eliminate \(x\) by subtracting Equation 2 from Equation 1:

\[
(-5x - 8y) - (-5x - 4y) = 15 - (-5)
\]

This simplifies to:

\[
-8y + 4y = 15 + 5
\]

So:

\[
-4y = 20
\]

Now, we can solve for \(y\) by dividing both sides by -4:

\[
y = \frac{20}{-4} = -5
\]

Now that we have \(y\), we can substitute it back into one of the original equations to find \(x\). We'll use Equation 2:

\[
-5x - 4(-5) = -5
\]

This simplifies to:

\[
-5x + 20 = -5
\]

Now, subtract 20 from both sides:

\[
-5x = -5 - 20
\]

\[
-5x = -25
\]

Now, divide both sides by -5:

\[
x = \frac{-25}{-5} = 5
\]

Now we have both values:

\[
x = 5, \quad y = -5
\]

The solution to the system of equations is:

\[
\boxed{(5, -5)}
\]