Sure! Let's solve the system of linear equations step by step:
Given the system of equations:
[tex]\[
\begin{cases}
4x - y = -9 \quad (1) \\
3x + 5y = -1 \quad (2)
\end{cases}
\][/tex]
### Step 1: Solve Equation (1) for [tex]\( y \)[/tex] in terms of [tex]\( x \)[/tex]
Starting with equation (1):
[tex]\[
4x - y = -9
\][/tex]
we can solve for [tex]\( y \)[/tex]:
[tex]\[
y = 4x + 9 \quad (3)
\][/tex]
### Step 2: Substitute Equation (3) into Equation (2)
Now, substitute the expression for [tex]\( y \)[/tex] from equation (3) into equation (2):
[tex]\[
3x + 5(4x + 9) = -1
\][/tex]
Simplify this equation:
[tex]\[
3x + 20x + 45 = -1
\][/tex]
Combine like terms:
[tex]\[
23x + 45 = -1
\][/tex]
Subtract 45 from both sides:
[tex]\[
23x = -46
\][/tex]
Divide both sides by 23:
[tex]\[
x = -2
\][/tex]
### Step 3: Substitute [tex]\( x = -2 \)[/tex] back into Equation (3)
Next, we substitute [tex]\( x = -2 \)[/tex] back into equation (3) to find [tex]\( y \)[/tex]:
[tex]\[
y = 4(-2) + 9
\][/tex]
Simplify:
[tex]\[
y = -8 + 9
\][/tex]
[tex]\[
y = 1
\][/tex]
### Conclusion
The solution to the system of equations is:
[tex]\[
\boxed{x = -2, y = 1}
\][/tex]
