Solve the system of equations.

Question

6x−3y=−6

9x−3y=−18
(1 point)
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Answer 1

To solve the system of equations:

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

We can start by manipulating the equations.

First, let's express each equation in a simpler form by dividing all terms in each equation by the coefficients of \( y \).

1. Divide the first equation by 3: \[ 2x - y = -2 \quad \text{(Equation 1)} \]

2. Divide the second equation by 3: \[ 3x - y = -6 \quad \text{(Equation 2)} \]

Now we have the following simplified system of equations:

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

Now let's subtract Equation 1 from Equation 2:

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

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

\[ 2(-4) - y = -2 \] \[ -8 - y = -2 \] \[ -y = -2 + 8 \] \[ -y = 6 \] \[ y = -6 \]

So, the solution to the system of equations is:

\[ (x, y) = (-4, -6) \]

Hence, the final answer is:

\[ \boxed{(-4, -6)} \]