Solve the system of equations.

6x−3y=−6
9x−3y=−18 (1 point)
(, )

1 answer

To solve the system of equations:

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

We can start by simplifying both equations.

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

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

Now we have a new system of equations:

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

Next, we can eliminate \(y\) by subtracting the first equation from the second: \[ (3x - y) - (2x - y) = -6 - (-2) \] This simplifies to: \[ 3x - 2x = -6 + 2 \] \[ x = -4 \]

Now, we can substitute \(x = -4\) back into one of the simplified equations to find \(y\). Let's use the first simplified equation: \[ 2x - y = -2 \] Substituting \(x\): \[ 2(-4) - y = -2 \] \[ -8 - y = -2 \] Adding \(8\) to both sides: \[ -y = 6 \] Multiplying both sides by -1: \[ y = -6 \]

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

Thus, the answer is \((-4, -6)\).