To solve the given system of equations:
[tex]\[
\begin{array}{l}
12x - 5y = -20 \\
y = x + 4 \\
\end{array}
\][/tex]
Let's go through the steps to find the values of [tex]\( x \)[/tex] and [tex]\( y \)[/tex].
### Step 1: Substitute the second equation into the first equation
The second equation is:
[tex]\[ y = x + 4 \][/tex]
We substitute [tex]\( y \)[/tex] from the second equation into the first equation:
[tex]\[
12x - 5(x + 4) = -20
\][/tex]
### Step 2: Simplify the equation
Now, distribute the [tex]\(-5\)[/tex] through the parentheses:
[tex]\[
12x - 5x - 20 = -20
\][/tex]
Combine like terms:
[tex]\[
7x - 20 = -20
\][/tex]
### Step 3: Solve for [tex]\( x \)[/tex]
Add [tex]\( 20 \)[/tex] to both sides of the equation:
[tex]\[
7x = 0
\][/tex]
Divide by [tex]\( 7 \)[/tex]:
[tex]\[
x = 0
\][/tex]
### Step 4: Solve for [tex]\( y \)[/tex]
Now that we have [tex]\( x = 0 \)[/tex], we substitute this value back into the second equation to find [tex]\( y \)[/tex]:
[tex]\[
y = x + 4
\][/tex]
Substitute [tex]\( x = 0 \)[/tex]:
[tex]\[
y = 0 + 4 = 4
\][/tex]
### Conclusion
The solution to the system of equations is:
[tex]\[
x = 0 \\
y = 4
\][/tex]
So, the values of [tex]\( x \)[/tex] and [tex]\( y \)[/tex] are:
[tex]\[
x = 0 \\
y = 4
\][/tex]
