Question

Solve the systems of equations using elimination.

x + y = -8
x - y = -6


(-1,7)


(-7,-1)


(-1,-7)


(-2,-4)

Answer 1

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

1. \( x + y = -8 \) (Equation 1)
2. \( x - y = -6 \) (Equation 2)

We can eliminate \(y\) by adding both equations together.

Adding (1) and (2):

\[
(x + y) + (x - y) = -8 + (-6)
\]

This simplifies to:

\[
2x = -14
\]

Now, divide both sides by 2:

\[
x = -7
\]

Now that we have \(x\), we can substitute \(x\) back into one of the original equations to find \(y\). We'll use Equation 1:

\[
-7 + y = -8
\]

To solve for \(y\), add 7 to both sides:

\[
y = -8 + 7
\]

\[
y = -1
\]

So the solution to the system of equations is:

\[
(x, y) = (-7, -1)
\]

Thus, the correct answer is:

\[
\boxed{(-7, -1)}
\]