Solve the system of equations.

−6x+2y=−32
4x+3y=−9 (1 point)
(, )

1 answer

To solve the system of equations:

  1. Equation 1: \(-6x + 2y = -32\)
  2. Equation 2: \(4x + 3y = -9\)

We can use the substitution or elimination method. Here, I'll use the elimination method.

First, let's rewrite the first equation in a simpler form. Divide the entire equation by 2:

\[ -3x + y = -16 \quad \text{(Equation 1 simplified)} \]

Now we have:

  1. \( -3x + y = -16 \)
  2. \( 4x + 3y = -9 \)

Next, we can express \(y\) from the first equation:

\[ y = 3x - 16 \]

Now substitute this expression for \(y\) into the second equation:

\[ 4x + 3(3x - 16) = -9 \]

Distributing:

\[ 4x + 9x - 48 = -9 \]

Combine like terms:

\[ 13x - 48 = -9 \]

Add 48 to both sides:

\[ 13x = 39 \]

Now, divide by 13:

\[ x = 3 \]

Now that we have \(x\), we can substitute it back into the equation for \(y\):

\[ y = 3(3) - 16 \] \[ y = 9 - 16 \] \[ y = -7 \]

Thus, the solution to the system of equations is:

\[ (x, y) = (3, -7) \]

So the answer is \((3, -7)\).