Systems of Linear Equations Unit Test

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Question
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 can use the substitution or elimination method. Here, I will use the substitution method.

First, we can solve Equation 2 for \(x\):

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

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 substitute \(y\) back to find \(x\):

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

Thus, the solution to the system of equations is:

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

The final answer is:

\[ (-4, 6) \]