Question

Solve using elimination.

–x + 4y = 7
–3x + 7y = 1

Answer 1

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

1. \(-x + 4y = 7\)
2. \(-3x + 7y = 1\)

First, we can manipulate the first equation to make the coefficients of \(x\) easier to align. We can multiply the entire first equation by 3 to eliminate \(x\) when we combine it with the second equation:

\[
3(-x + 4y) = 3(7)
\]

This gives us:

\[
-3x + 12y = 21 \quad \text{(Equation 3)}
\]

Now our system of equations looks like this:

3. \(-3x + 12y = 21\)
4. \(-3x + 7y = 1\)

Next, we will subtract Equation 4 from Equation 3 to eliminate \(x\):

\[
(-3x + 12y) - (-3x + 7y) = 21 - 1
\]

Simplifying this gives:

\[
12y - 7y = 20
\]

\[
5y = 20
\]

Now, divide both sides by 5:

\[
y = 4
\]

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

\[
-x + 4(4) = 7
\]

This simplifies to:

\[
-x + 16 = 7
\]

Subtract 16 from both sides:

\[
-x = 7 - 16
\]

\[
-x = -9
\]

Multiplying both sides by -1 gives:

\[
x = 9
\]

Thus, the solution to the system of equations is:

\[
\boxed{(9, 4)}
\]