Question

Solve using elimination.

–3x + 6y = 15
x + 3y = –15

Answer 1

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

1) \(-3x + 6y = 15\)
2) \(x + 3y = -15\)

To use the elimination method, we can multiply the second equation by 3 to eliminate \(x\):

\[
3(x + 3y) = 3(-15)
\]

This simplifies to:

\[
3x + 9y = -45
\]

Now, we rewrite our system with this new equation:

1) \(-3x + 6y = 15\)
2) \(3x + 9y = -45\)

Next, we add both equations together:

\[
(-3x + 6y) + (3x + 9y) = 15 - 45
\]

When we combine like terms, we have:

\[
0x + 15y = -30
\]

This simplifies to:

\[
15y = -30
\]

Now, we solve for \(y\):

\[
y = \frac{-30}{15} = -2
\]

Next, we substitute \(y = -2\) back into one of the original equations to find \(x\). We can use the second equation:

\[
x + 3(-2) = -15
\]

This simplifies to:

\[
x - 6 = -15
\]

Adding 6 to both sides gives:

\[
x = -15 + 6 = -9
\]

We have found the solution:

\[
x = -9, \quad y = -2
\]

Thus, the solution to the given system of equations is:

\[
\boxed{(-9, -2)}
\]