Question

Solve the system of equations. 5x–4y=–44 5 𝑥 – 4 𝑦 = – 44 –x+3y=22 – 𝑥 + 3 𝑦 = 22 (1 point) (, )

Answer 1

To solve the system of equations:

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

Let's use the substitution or elimination method to solve this system.

### Step 1: Solve one equation for one variable
From Equation 2, solve for \( x \):

\[
-x + 3y = 22
\]

\[
-x = 22 - 3y
\]

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

### Step 2: Substitute Equation 3 into Equation 1
Substitute (Equation 3) into Equation 1:

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

Distribute the 5:

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

Combine like terms:

\[
11y - 110 = -44
\]

Add 110 to both sides:

\[
11y = 110 - 44
\]

\[
11y = 66
\]

Divide by 11:

\[
y = 6
\]

### Step 3: Substitute \( y \) back to find \( x \)
Now use the value of \( y \) in Equation 3:

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

\[
x = 18 - 22
\]

\[
x = -4
\]

### Step 4: Write the solution
The solution to the system of equations is:

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

### Final Answer
\((-4, 6)\)