Question

solve the system of linear equations by elimination.
$x + y = 3$
$x - y = 1$
solution: (\square, \square)

Explanation:

Step1: Add the two equations

To eliminate \( y \), we add the equations \( x + y = 3 \) and \( x - y = 1 \).
\[

$$\begin{align*} (x + y) + (x - y) &= 3 + 1\\ x + y + x - y &= 4\\ 2x &= 4 \end{align*}$$

\]

Step2: Solve for \( x \)

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

Step3: Substitute \( x = 2 \) into \( x + y = 3 \)

Substitute \( x = 2 \) into the first equation \( x + y = 3 \).
\[
2 + y = 3
\]

Step4: Solve for \( y \)

Subtract 2 from both sides of \( 2 + y = 3 \).
\[
y=3 - 2=1
\]

Answer:

\((2, 1)\)