Question

Solve using elimination.

–2x − 2y = 8
–4x − 8y = –8

Answer 1

To solve the system of equations using elimination, we first write the equations:

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

To use elimination, we want to manipulate these equations so that when we add or subtract them, one variable cancels out.

Let's manipulate Equation 1. We can multiply Equation 1 by 2 to make the coefficients of \(x\) in both equations match:

\[
2(-2x - 2y) = 2(8)
\]

This gives us:

\[
-4x - 4y = 16 \quad \text{(Equation 3)}
\]

Now we have:

1. \(-4x - 4y = 16\) (Equation 3)
2. \(-4x - 8y = -8\) (Equation 2)

Next, we can eliminate \(x\) by subtracting Equation 2 from Equation 3:

\[
(-4x - 4y) - (-4x - 8y) = 16 - (-8)
\]

This simplifies to:

\[
-4y + 8y = 16 + 8
\]

Combine the terms:

\[
4y = 24
\]

Now, divide by 4:

\[
y = 6
\]

Next, we substitute \(y = 6\) back into one of the original equations to find \(x\). Let's use Equation 1:

\[
-2x - 2(6) = 8
\]
\[
-2x - 12 = 8
\]

Adding 12 to both sides:

\[
-2x = 20
\]

Now, divide by -2:

\[
x = -10
\]

Thus, the solution to the system of equations is:

\[
x = -10, \quad y = 6
\]

In summary, the solution is:

\[
\boxed{(-10, 6)}
\]