Sure, let's solve this system of linear equations step-by-step:
The system of equations is:
[tex]\[
\begin{cases}
y = -x + 8 \quad \text{(1)} \\
3x - 2y = 4 \quad \text{(2)}
\end{cases}
\][/tex]
Step 1: Substitute equation (1) into equation (2).
From equation (1), we have [tex]\( y = -x + 8 \)[/tex]. We will substitute this expression for [tex]\( y \)[/tex] in equation (2):
[tex]\[ 3x - 2(-x + 8) = 4 \][/tex]
Step 2: Simplify the equation.
First, distribute the [tex]\( -2 \)[/tex]:
[tex]\[ 3x + 2x - 16 = 4 \][/tex]
Next, combine like terms:
[tex]\[ 5x - 16 = 4 \][/tex]
Step 3: Solve for [tex]\( x \)[/tex].
Add 16 to both sides of the equation:
[tex]\[ 5x = 20 \][/tex]
Then, divide both sides by 5:
[tex]\[ x = 4 \][/tex]
Step 4: Solve for [tex]\( y \)[/tex].
Substitute [tex]\( x = 4 \)[/tex] back into equation (1):
[tex]\[ y = -4 + 8 \][/tex]
This simplifies to:
[tex]\[ y = 4 \][/tex]
Thus, the solution to the system of equations is:
[tex]\[ x = 4, \quad y = 4 \][/tex]
So, the solution is [tex]\((4, 4)\)[/tex].
