Question

x + y = 5\
x - y = 1\
show your work

Explanation:

Step1: Add the two equations

To eliminate \( y \), we add the equations \( x + y = 5 \) and \( x - y = 1 \).
\[

$$\begin{align*} (x + y) + (x - y) &= 5 + 1\\ x + y + x - y &= 6\\ 2x &= 6 \end{align*}$$

\]

Step2: Solve for \( x \)

Divide both sides of \( 2x = 6 \) by 2.
\[
x=\frac{6}{2}=3
\]

Step3: Substitute \( x = 3 \) into \( x + y = 5 \)

Substitute \( x = 3 \) into the first equation \( x + y = 5 \) to find \( y \).
\[
3 + y = 5
\]
Subtract 3 from both sides:
\[
y = 5 - 3 = 2
\]

Answer:

The solution to the system of equations is \( x = 3 \) and \( y = 2 \).