Question

Solve using elimination.

10x + 10y = –10
–9x − 10y = 19

Answer 1

To solve the equations using elimination, we start with the two given equations:

1) \( 10x + 10y = -10 \)
2) \( -9x - 10y = 19 \)

First, we can manipulate the first equation to make the elimination process easier. We can divide the entire first equation by 10:

\[
x + y = -1
\]

Now, we can rewrite the equations as:

1) \( x + y = -1 \)
2) \( -9x - 10y = 19 \)

Next, we can manipulate the first equation to isolate \(x\):

\[
x = -1 - y
\]

Now, we can substitute this expression for \(x\) into the second equation. Replacing \(x\) in equation 2 gives:

\[
-9(-1 - y) - 10y = 19
\]

Distributing \(-9\):

\[
9 + 9y - 10y = 19
\]

Combining like terms:

\[
9 - y = 19
\]

Now, we can isolate \(y\):

\[
-y = 19 - 9
\]
\[
-y = 10
\]
\[
y = -10
\]

Now that we have \(y\), we can substitute it back into the equation we found for \(x\):

\[
x = -1 - y
\]
\[
x = -1 - (-10)
\]
\[
x = -1 + 10
\]
\[
x = 9
\]

So, the solution to the system of equations is:

\[
x = 9, \quad y = -10
\]

Lastly, we can write the solution as an ordered pair:

\[
\boxed{(9, -10)}
\]