Question

Solve using elimination.

10x − 10y = –20
–10x + 6y = –20

Answer 1

To solve the system of equations using elimination, we start with the following equations:

1. \( 10x - 10y = -20 \) (Equation 1)
2. \( -10x + 6y = -20 \) (Equation 2)

We can eliminate \( x \) by adding both equations together. Notice that the coefficients of \( x \) in the two equations are opposites.

Adding Equation 1 and Equation 2:

\[
(10x - 10y) + (-10x + 6y) = -20 + (-20)
\]

Simplifying this:

\[
0x - 4y = -40
\]

This simplifies to:

\[
-4y = -40
\]

Now we can solve for \( y \) by dividing both sides by -4:

\[
y = \frac{-40}{-4} = 10
\]

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

\[
10x - 10(10) = -20
\]

This simplifies to:

\[
10x - 100 = -20
\]

Adding 100 to both sides:

\[
10x = 80
\]

Now we can solve for \( x \):

\[
x = \frac{80}{10} = 8
\]

So, the solution to the system of equations is:

\[
x = 8, \quad y = 10
\]

Thus, the solution is:

\[
\boxed{(8, 10)}
\]