Question

Solve the system of equations.
5x–4y=–44

–x+3y=22
(1 point)
(
,
)

Answer 1

To solve the system of equations:

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

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

First, we will express one variable in terms of the other using Equation 2. From Equation 2, we can solve for \( x \):

\[
-x + 3y = 22
\]

Rearranging gives us:

\[
-x = 22 - 3y
\]

\[
x = 3y - 22 \quad \text{(Equation 3)}
\]

Next, we substitute Equation 3 into Equation 1:

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

Expanding this gives:

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

Combining like terms:

\[
11y - 110 = -44
\]

Now, add 110 to both sides:

\[
11y = 66
\]

Dividing both sides by 11:

\[
y = 6
\]

Now that we have \( y \), we can substitute back into Equation 3 to find \( x \):

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

\[
x = 18 - 22
\]

\[
x = -4
\]

Thus, the solution to the system of equations is:

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

Final answer: \((-4, 6)\)