To solve the system of equations using substitution, follow these steps:
Given equations:
1. [tex]\( y = x - 4 \)[/tex]
2. [tex]\( 4x + y = 26 \)[/tex]
### Step 1: Substitute the expression for [tex]\( y \)[/tex] from the first equation into the second equation.
From the first equation, we can express [tex]\( y \)[/tex] in terms of [tex]\( x \)[/tex]:
[tex]\[ y = x - 4 \][/tex]
Now, substitute [tex]\( y = x - 4 \)[/tex] into the second equation:
[tex]\[ 4x + (x - 4) = 26 \][/tex]
### Step 2: Simplify the equation and solve for [tex]\( x \)[/tex].
Combine like terms:
[tex]\[ 4x + x - 4 = 26 \][/tex]
[tex]\[ 5x - 4 = 26 \][/tex]
Add 4 to both sides of the equation:
[tex]\[ 5x = 30 \][/tex]
Divide both sides by 5:
[tex]\[ x = 6 \][/tex]
### Step 3: Solve for [tex]\( y \)[/tex] using the value of [tex]\( x \)[/tex].
Substitute [tex]\( x = 6 \)[/tex] back into the first equation:
[tex]\[ y = 6 - 4 \][/tex]
[tex]\[ y = 2 \][/tex]
### Step 4: Write the solution as an ordered pair.
The solution to the system of equations is:
[tex]\[ (x, y) = (6, 2) \][/tex]
Thus, the answer is [tex]\((6, 2)\)[/tex].
