Sure, let's solve the system of equations using the elimination method. The system we have is:
[tex]\[
\begin{cases}
x - 4y = -13 \quad \text{(Equation 1)} \\
2x + 4y = 10 \quad \text{(Equation 2)}
\end{cases}
\][/tex]
### Step 1: Add the two equations to eliminate [tex]\( y \)[/tex]
First, we add Equation 1 and Equation 2 together:
[tex]\[
(x - 4y) + (2x + 4y) = -13 + 10
\][/tex]
Simplify the left-hand side:
[tex]\[
x + 2x - 4y + 4y = -13 + 10
\][/tex]
The [tex]\( y \)[/tex] terms cancel each other out:
[tex]\[
3x = -3
\][/tex]
### Step 2: Solve for [tex]\( x \)[/tex]
Now, solve the equation [tex]\( 3x = -3 \)[/tex] for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{-3}{3} = -1
\][/tex]
### Step 3: Substitute [tex]\( x = -1 \)[/tex] back into one of the original equations to solve for [tex]\( y \)[/tex]
We can substitute [tex]\( x = -1 \)[/tex] into Equation 1:
[tex]\[
x - 4y = -13
\][/tex]
Substitute [tex]\( x \)[/tex] with [tex]\(-1\)[/tex]:
[tex]\[
-1 - 4y = -13
\][/tex]
Solve for [tex]\( y \)[/tex]:
[tex]\[
-4y = -13 + 1
\][/tex]
[tex]\[
-4y = -12
\][/tex]
[tex]\[
y = \frac{-12}{-4} = 3
\][/tex]
### Step 4: Write the solution as an ordered pair
The solution to the system of equations is:
[tex]\[
(x, y) = (-1, 3)
\][/tex]
Hence, the solution of the system is [tex]\((-1, 3)\)[/tex].
