Question

Solve the systems of equations using elimination.

-3x + y = -9
x - 2y = -12


(-10,3)


(-6,-9)


(6,9)


(6,-10)

Answer 1

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

1. \(-3x + y = -9\) (Equation 1)
2. \(x - 2y = -12\) (Equation 2)

First, we can manipulate these equations to eliminate one of the variables.

Let's rearrange both equations to work with easier coefficients:

From Equation 1:
\[
y = 3x - 9
\]

From Equation 2:
\[
x = 2y - 12
\]

Now, let's manipulate one of the original equations for elimination. We can multiply Equation 1 by 2 to align the coefficients of \(y\):

Multiply Equation 1 by 2:
\[
-6x + 2y = -18 \quad \text{(Equation 3)}
\]

Now we have:
1. \( -6x + 2y = -18 \) (Equation 3)
2. \( x - 2y = -12 \) (Equation 2)

Now we can add Equation 3 and Equation 2 together:

\[
(-6x + 2y) + (x - 2y) = -18 - 12
\]
This simplifies to:
\[
-6x + x + 2y - 2y = -30
\]
\[
-5x = -30
\]
\[
x = 6
\]

Now we can substitute \(x = 6\) back into one of the original equations to find \(y\). Let's use Equation 1:
\[
-3(6) + y = -9
\]
\[
-18 + y = -9
\]
\[
y = -9 + 18
\]
\[
y = 9
\]

The solution to the system of equations is:
\[
(x, y) = (6, 9)
\]

Thus, the solution in your answer choices is:
**(6, 9)**.