Question

Solve using elimination.

–3x + 4y = 4
–6x + 6y = –6

Answer 1

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

1) \(-3x + 4y = 4\)
2) \(-6x + 6y = -6\)

First, we can manipulate the equations to facilitate elimination. We can multiply the first equation by 2 to align the coefficients of \(x\):

\[
2(-3x + 4y) = 2(4)
\]

This gives us:

\[
-6x + 8y = 8 \quad (3)
\]

Now we rewrite our system of equations:

3) \(-6x + 8y = 8\)
4) \(-6x + 6y = -6\)

Next, we can subtract equation (4) from equation (3):

\[
(-6x + 8y) - (-6x + 6y) = 8 - (-6)
\]

This simplifies to:

\[
8y - 6y = 8 + 6
\]
\[
2y = 14
\]
\[
y = 7
\]

Now that we have the value of \(y\), we can substitute it back into one of the original equations to find \(x\). Let's use equation (1):

\[
-3x + 4(7) = 4
\]
\[
-3x + 28 = 4
\]
\[
-3x = 4 - 28
\]
\[
-3x = -24
\]
\[
x = 8
\]

Thus, the solution to the system of equations is:

\[
\boxed{(8, 7)}
\]