Question

Solve using elimination.

9x + 10y = 8
–8x − 10y = –16

Answer 1

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

1) \( 9x + 10y = 8 \)
2) \( -8x - 10y = -16 \)

First, we will add the two equations together to eliminate \(y\):

\[
(9x + 10y) + (-8x - 10y) = 8 + (-16)
\]

This simplifies to:

\[
(9x - 8x) + (10y - 10y) = 8 - 16
\]

\[
x + 0y = -8
\]

\[
x = -8
\]

Now that we have the value of \(x\), we will substitute it back into one of the original equations to find the value of \(y\). We will use the first equation:

\[
9(-8) + 10y = 8
\]

This simplifies to:

\[
-72 + 10y = 8
\]

Next, we add 72 to both sides:

\[
10y = 8 + 72
\]

\[
10y = 80
\]

Now, divide both sides by 10:

\[
y = 8
\]

So the solution to the system of equations is:

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

The final solution can be written as the coordinate:

\[
(-8, 8)
\]