To solve the given system of simultaneous equations:
[tex]\[
\begin{cases}
x + y = 5 \\
x - y = 1
\end{cases}
\][/tex]
we can use either the substitution method or the elimination method. Here, I will use the elimination method:
1. Write down the equations:
[tex]\[
1) \quad x + y = 5
\][/tex]
[tex]\[
2) \quad x - y = 1
\][/tex]
2. Add the two equations together to eliminate [tex]\( y \)[/tex]:
[tex]\[
(x + y) + (x - y) = 5 + 1
\][/tex]
Simplifying this, we get:
[tex]\[
2x = 6
\][/tex]
3. Solve for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{6}{2} = 3
\][/tex]
4. Substitute [tex]\( x = 3 \)[/tex] back into one of the original equations to solve for [tex]\( y \)[/tex]. We can use the first equation [tex]\( x + y = 5 \)[/tex]:
[tex]\[
3 + y = 5
\][/tex]
5. Solve for [tex]\( y \)[/tex]:
[tex]\[
y = 5 - 3 = 2
\][/tex]
So, the solution to the system of equations is:
[tex]\[
\boxed{(x, y) = (3, 2)}
\][/tex]
This gives us the values [tex]\( x = 3 \)[/tex] and [tex]\( y = 2 \)[/tex].
