To solve the system of equations:
[tex]\[
\begin{cases}
4x - y = -38 \\
x + y = 3
\end{cases}
\][/tex]
we will use the method of substitution or elimination. Let's go through the steps in detail:
Step 1: Solve one of the equations for one variable.
Let's solve the second equation for [tex]\( y \)[/tex]:
[tex]\[
x + y = 3
\][/tex]
Subtract [tex]\( x \)[/tex] from both sides:
[tex]\[
y = 3 - x
\][/tex]
Step 2: Substitute this expression for [tex]\( y \)[/tex] into the first equation.
Now substitute [tex]\( y = 3 - x \)[/tex] into the first equation [tex]\( 4x - y = -38 \)[/tex]:
[tex]\[
4x - (3 - x) = -38
\][/tex]
Simplify inside the parentheses:
[tex]\[
4x - 3 + x = -38
\][/tex]
Combine like terms:
[tex]\[
5x - 3 = -38
\][/tex]
Step 3: Solve for [tex]\( x \)[/tex].
Add 3 to both sides to isolate the term with [tex]\( x \)[/tex]:
[tex]\[
5x = -35
\][/tex]
Divide both sides by 5:
[tex]\[
x = -7
\][/tex]
Step 4: Substitute [tex]\( x = -7 \)[/tex] back into the expression for [tex]\( y \)[/tex] to find [tex]\( y \)[/tex].
Substitute [tex]\( x = -7 \)[/tex] into the equation [tex]\( y = 3 - x \)[/tex]:
[tex]\[
y = 3 - (-7)
\][/tex]
Simplify:
[tex]\[
y = 3 + 7
\][/tex]
[tex]\[
y = 10
\][/tex]
Conclusion:
The solution to the system of equations is:
[tex]\[
x = -7
\][/tex]
[tex]\[
y = 10
\][/tex]
Therefore, the values in the boxes should be:
[tex]\[
x = -7 \quad \text{and} \quad y = 10
\][/tex]
