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6x−3y=−6

9x−3y=−18
(1 point)
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1 answer

To solve the system of equations given by:

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

Let's first simplify these equations.

For Equation 1, we can divide all terms by 3:

\[ 2x - y = -2 \]

For Equation 2, we can also divide all terms by 3:

\[ 3x - y = -6 \]

Now we have the simplified system:

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

Next, we can solve for \( y \) in both equations. Starting with Equation 1:

\[ y = 2x + 2 \]

Now substituting this expression for \( y \) into Equation 2:

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

Simplifying this gives:

\[ 3x - 2x - 2 = -6 \] \[ x - 2 = -6 \] \[ x = -4 \]

Now substituting \( x = -4 \) back into the expression for \( y \):

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

Thus, the solution to the system of equations is:

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

So, the answer is:

\[ (-4, -6) \]