Question

Solve using elimination.

–2x − 5y = 5
–x + 2y = –20

Answer 1

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

1. \(-2x - 5y = 5\) (Equation 1)
2. \(-x + 2y = -20\) (Equation 2)

First, we can manipulate Equation 2 to align the coefficients of \(x\) with those in Equation 1. We can multiply Equation 2 by 2 to make the coefficient of \(x\) match that in Equation 1:

\[
2(-x + 2y) = 2(-20)
\]

This results in:

\[
-2x + 4y = -40 \quad \text{(Equation 3)}
\]

Now we have:

1. \(-2x - 5y = 5\) (Equation 1)
2. \(-2x + 4y = -40\) (Equation 3)

Next, we can eliminate \(x\) by subtracting Equation 1 from Equation 3:

\[
(-2x + 4y) - (-2x - 5y) = -40 - 5
\]

This simplifies to:

\[
4y + 5y = -45
\]

Combine like terms:

\[
9y = -45
\]

Now, divide by 9:

\[
y = -5
\]

Now that we have \(y\), we can substitute it back into either original equation to find \(x\). We'll use Equation 2 for substitution:

\[
-x + 2(-5) = -20
\]

This gives us:

\[
-x - 10 = -20
\]

Now, add 10 to both sides:

\[
-x = -10
\]

Multiply by -1:

\[
x = 10
\]

The solution to the system of equations is:

\[
(x, y) = (10, -5)
\]

Final answer:

\[
\boxed{(10, -5)}
\]