Question

Systems of Linear Equations Unit Test
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Question
Solve the system of equations.
6x−3y=−6

9x−3y=−18
(1 point)
(
,
)

Answer 1

To solve the system of equations:

1. \(6x - 3y = -6\) (Equation 1)
2. \(9x - 3y = -18\) (Equation 2)

We can start by rewriting both equations to see if they are equivalent or have a unique solution.

Let's simplify each equation.

From Equation 1:
\[
6x - 3y = -6
\]
Divide the entire equation by 3:
\[
2x - y = -2 \quad \text{(Equation 1 simplified)}
\]

From Equation 2:
\[
9x - 3y = -18
\]
Divide the entire equation by 3:
\[
3x - y = -6 \quad \text{(Equation 2 simplified)}
\]

Now, we can compare the two simplified equations:

1. \(2x - y = -2\)
2. \(3x - y = -6\)

Next, let's use the method of elimination. Subtract Equation 1 from Equation 2:

\[
(3x - y) - (2x - y) = -6 - (-2)
\]
This simplifies to:
\[
3x - 2x = -6 + 2
\]
Which gives:
\[
x = -4
\]

Now, substitute \(x = -4\) back into one of the original equations to find \(y\). We'll use Equation 1:

\[
6(-4) - 3y = -6
\]
This simplifies to:
\[
-24 - 3y = -6
\]
Adding 24 to both sides:
\[
-3y = 18
\]
Dividing by -3:
\[
y = -6
\]

Thus, the solution to the system of equations is:
\[
(x, y) = (-4, -6)
\]

The final answer is:
\[
\boxed{(-4, -6)}
\]