Question

Systems of Linear Equations Unit Test
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Question
Solve the system of equations.
5x–4y=–44

–x+3y=22

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, I'll use the elimination method:

First, let's express Equation 2 in a form where we can eliminate one variable. We can multiply Equation 2 by 5 to align the coefficients of \( x \):

\[
5(-x + 3y) = 5(22)
\]
This simplifies to:

\[
-5x + 15y = 110 \quad \text{(Equation 3)}
\]

Now we have:

1. \( 5x - 4y = -44 \) (Equation 1)
2. \( -5x + 15y = 110 \) (Equation 3)

Next, we can add Equation 1 and Equation 3:

\[
(5x - 4y) + (-5x + 15y) = -44 + 110
\]

This simplifies to:

\[
0x + 11y = 66
\]

Now, solve for \( y \):

\[
11y = 66
\]
\[
y = \frac{66}{11} = 6
\]

Now that we have \( y \), substitute \( y = 6 \) back into one of the original equations to find \( x \). Let's use Equation 2:

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

This simplifies to:

\[
-x + 18 = 22
\]
\[
-x = 22 - 18
\]
\[
-x = 4
\]
\[
x = -4
\]

So, the solution to the system of equations is:

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