Question

Solve using elimination.

–10x − y = 17
–3x − 3y = –3

Answer 1

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

1. \(-10x - y = 17\) (Equation 1)
2. \(-3x - 3y = -3\) (Equation 2)

First, we can simplify Equation 2 by dividing each term by -3:

\[
x + y = 1 \quad (Equation 3)
\]

Now we have:

1. \(-10x - y = 17\) (Equation 1)
2. \(x + y = 1\) (Equation 3)

Next, we can eliminate \(y\) by adding Equations 1 and 3. To do that, we can rearrange Equation 3 to express \(y\):

\[
y = 1 - x
\]

Now substitute this expression for \(y\) back into Equation 1:

\[
-10x - (1 - x) = 17
\]

Now simplify the equation:

\[
-10x - 1 + x = 17
\]
\[
-9x - 1 = 17
\]

Next, add 1 to both sides:

\[
-9x = 18
\]

Now, divide by -9:

\[
x = -2
\]

Now that we have \(x\), we can find \(y\) using Equation 3:

\[
x + y = 1
\]
\[
-2 + y = 1
\]
\[
y = 1 + 2 = 3
\]

So, the solution to the system of equations is:

\[
\boxed{(-2, 3)}
\]