Solve the system of equations.

5x–4y=–44
–x+3y=22 (1 point)
(, )

1 answer

To solve the system of equations:

  1. \( 5x - 4y = -44 \) (Equation 1)
  2. \( -x + 3y = 22 \) (Equation 2)

We'll start by solving Equation 2 for \( x \):

\[ -x + 3y = 22 \] \[ x = 3y - 22 \]

Now, substitute \( x \) in Equation 1:

\[ 5(3y - 22) - 4y = -44 \]

Distribute \( 5 \):

\[ 15y - 110 - 4y = -44 \]

Combine like terms:

\[ 11y - 110 = -44 \]

Add \( 110 \) to both sides:

\[ 11y = 66 \]

Now, divide by \( 11 \):

\[ y = 6 \]

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

\[ x = 3(6) - 22 \] \[ x = 18 - 22 \] \[ x = -4 \]

Thus, the solution to the system of equations is:

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

Final answer:

\[ (-4, 6) \]