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 either substitution or elimination. Here, I will use the elimination method.

First, we can multiply Equation 2 by 5 to align the coefficients of \(x\):

\[
5(-x + 3y) = 5(22)
\]
\[
-5x + 15y = 110 \quad \text{(Equation 3)}
\]

Now we have the modified system:

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

Next, we will add Equations 1 and 3:

\[
(5x - 4y) + (-5x + 15y) = -44 + 110
\]
\[
(5x - 5x) + (-4y + 15y) = 66
\]
\[
0 + 11y = 66
\]
\[
11y = 66
\]
\[
y = \frac{66}{11} = 6
\]

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

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

Thus, the solution to the system of equations is:

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