Question

solve the system.
x + y = 4
x - y = 4

Explanation:

Step1: Add the two equations

Add the equations \(x + y = 4\) and \(x - y = 4\) together.
\[

$$\begin{align*} (x + y)+(x - y)&=4 + 4\\ x + y+x - y&=8\\ 2x&=8 \end{align*}$$

\]

Step2: Solve for x

Divide both sides of \(2x = 8\) by 2.
\[
x=\frac{8}{2}=4
\]

Step3: Substitute x into first equation

Substitute \(x = 4\) into \(x + y = 4\).
\[
4 + y = 4
\]

Step4: Solve for y

Subtract 4 from both sides of \(4 + y = 4\).
\[
y=4 - 4=0
\]

Answer:

The solution to the system is \(x = 4\) and \(y = 0\)