Question

or
Solve using elimination.

–7x − 5y = –16
–7x − 8y = –13

(
,
)

Answer 1

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

1. \(-7x - 5y = -16\) \quad (Equation 1)
2. \(-7x - 8y = -13\) \quad (Equation 2)

To eliminate \(x\), we can subtract Equation 1 from Equation 2:

\[
(-7x - 8y) - (-7x - 5y) = -13 - (-16)
\]

This simplifies to:

\[
-8y + 5y = -13 + 16
\]

\[
-3y = 3
\]

Now, divide both sides by -3:

\[
y = -1
\]

Next, we substitute \(y = -1\) back into one of the original equations to solve for \(x\). We'll use Equation 1:

\[
-7x - 5(-1) = -16
\]

This simplifies to:

\[
-7x + 5 = -16
\]

Now, subtract 5 from both sides:

\[
-7x = -21
\]

Now, divide by -7:

\[
x = 3
\]

Thus, the solution to the system of equations is:

\((x, y) = (3, -1)\)

So the final answer is:

\((3, -1)\)