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 \( x - y = 1 \).

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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:

\((2, 1)\)