Solving by Elimination

Elimination means adding or subtracting equations to cancel one variable. For the same system:

$x + y = 10$

$x - y = 4$

Add the equations: $(x + y) + (x - y) = 10 + 4$. The $y$ terms cancel, giving $2x = 14$, so $x = 7$. Substitute back to find $y = 3$.