Question

Solve using elimination.

–x + 5y = 17
2x + y = 10

Answer 1

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

1) \(-x + 5y = 17\)
2) \(2x + y = 10\)

First, let's manipulate the equations so that we can eliminate one of the variables. We will eliminate \(x\).

We can multiply the first equation by 2 to align the coefficients of \(x\):

\[
2(-x + 5y) = 2(17)
\]

This simplifies to:

\[
-2x + 10y = 34 \tag{3}
\]

Now we have:

1. \(-2x + 10y = 34\) (equation 3)
2. \(2x + y = 10\) (equation 2)

Next, let's add equations (3) and (2) to eliminate \(x\):

\[
(-2x + 10y) + (2x + y) = 34 + 10
\]

The \(x\) terms cancel out:

\[
10y + y = 44
\]

Combining like terms gives:

\[
11y = 44
\]

Now, divide both sides by 11:

\[
y = 4
\]

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

\[
2x + y = 10
\]

Substituting \(y = 4\):

\[
2x + 4 = 10
\]

Now, isolate \(2x\) by subtracting 4 from both sides:

\[
2x = 6
\]

Dividing both sides by 2 gives:

\[
x = 3
\]

Thus, the solution to the system of equations is:

\[
(x, y) = (3, 4)
\]

To summarize, the solution is \( \boxed{(3, 4)} \).