Question

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

–x+3y=22
(1 point)
(
,
)

Answer 1

To solve the system of equations, we can use the method of substitution or elimination. Let's use the elimination method for this problem.

The given equations are:

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

Let's first manipulate the second equation to express \( x \) in terms of \( y \):

From the second equation:
\[
-x + 3y = 22
\]
Adding \( x \) to both sides gives:
\[
3y = x + 22
\]
Now, we can solve for \( x \):
\[
x = 3y - 22
\]

Next, we substitute \( x \) in the first equation with \( 3y - 22 \):
\[
5(3y - 22) - 4y = -44
\]
Distributing \( 5 \) gives:
\[
15y - 110 - 4y = -44
\]
Combining like terms:
\[
15y - 4y - 110 = -44
\]
\[
11y - 110 = -44
\]
Now add \( 110 \) to both sides:
\[
11y = 66
\]
Now divide by \( 11 \):
\[
y = 6
\]

Now that we have \( y \), we can find \( x \) using the expression \( x = 3y - 22 \):
\[
x = 3(6) - 22
\]
\[
x = 18 - 22
\]
\[
x = -4
\]

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

So the final answer is:
\[
\boxed{(-4, 6)}
\]