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

\((-4, 6)\)