Answer :

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].