Sure, let's solve the given system of simultaneous equations:
[tex]\[
\begin{aligned}
1. \quad 3x - y &= 9 \\
2. \quad x + 5y &= 5
\end{aligned}
\][/tex]
### Step-by-Step Solution:
1. Express [tex]\( y \)[/tex] in terms of [tex]\( x \)[/tex] from Equation 1:
From the first equation:
[tex]\[
3x - y = 9
\][/tex]
Rearrange to express [tex]\( y \)[/tex] in terms of [tex]\( x \)[/tex]:
[tex]\[
y = 3x - 9
\][/tex]
2. Substitute [tex]\( y \)[/tex] in the second equation:
Substitute [tex]\( y = 3x - 9 \)[/tex] into the second equation:
[tex]\[
x + 5(3x - 9) = 5
\][/tex]
3. Solve for [tex]\( x \)[/tex]:
Simplify the equation:
[tex]\[
x + 15x - 45 = 5
\][/tex]
Combine like terms:
[tex]\[
16x - 45 = 5
\][/tex]
Add 45 to both sides:
[tex]\[
16x = 50
\][/tex]
Divide by 16:
[tex]\[
x = \frac{50}{16} = 3.125
\][/tex]
4. Substitute [tex]\( x \)[/tex] back into the expression for [tex]\( y \)[/tex]:
We know:
[tex]\[
y = 3x - 9
\][/tex]
Substitute [tex]\( x = 3.125 \)[/tex]:
[tex]\[
y = 3(3.125) - 9
\][/tex]
Calculate the value:
[tex]\[
y = 9.375 - 9
\][/tex]
Simplify:
[tex]\[
y = 0.375
\][/tex]
Thus, the solution to the system of equations is:
[tex]\[
\boxed{(x, y) = (3.125, 0.375)}
\][/tex]
