Question

Solve using elimination.

–x − 5y = –9
6x − y = –8

(
,
)

Answer 1

To solve the system of equations using the elimination method, let's first write down the equations:

1) \(-x - 5y = -9\)

2) \(6x - y = -8\)

We will aim to eliminate one of the variables. Let's eliminate \(y\). To do this, we can multiply the first equation by 1 to keep it the same, and multiply the second equation by 5 to match the coefficients of \(y\):

1) \(-x - 5y = -9\) (unchanged)

2) \(30x - 5y = -40\) (after multiplying by 5)

Now we have:

1) \(-x - 5y = -9\)

2) \(30x - 5y = -40\)

Next, we will subtract the first equation from the second equation to eliminate \(y\):

\[
(30x - 5y) - (-x - 5y) = -40 - (-9)
\]

This simplifies to:

\[
30x - 5y + x + 5y = -40 + 9
\]

Combining like terms:

\[
31x = -31
\]

Now, divide by 31:

\[
x = -1
\]

Next, substitute \(x = -1\) back into one of the original equations to find \(y\). We'll use the second equation:

\[
6(-1) - y = -8
\]

This simplifies to:

\[
-6 - y = -8
\]

Now, isolate \(y\):

\[
-y = -8 + 6
\]
\[
-y = -2
\]

So:

\[
y = 2
\]

The solution of the system of equations is:

\[
(x, y) = (-1, 2)
\]

**Final Answer: \((-1, 2)\)**