If 3x + 2y = 22 and x - 2y = 2, what is the value of x?

The $y$-terms have opposite coefficients, $+2y$ and $-2y$, so adding the equations eliminates $y$: $(3x + 2y) + (x - 2y) = 22 + 2$, which gives $4x = 24$ and $x = 6$. As a check, substitute into the second equation: $6 - 2y = 2$, so $y = 2$, and the first equation gives $18 + 4 = 22$, which works. Common wrong answers include 5 or 8, which come from adding $22 + 2$ incorrectly or from subtracting the equations instead, which would leave $2x + 4y = 20$ and fail to eliminate a variable.