If 3x + 2y = 16 and x - 2y = -4, what is the value of x?

The $y$-terms are $+2y$ and $-2y$, so they cancel when the equations are added: $(3x + 2y) + (x - 2y) = 16 + (-4)$, which gives $4x = 12$ and $x = 3$. Check: from the second equation, $3 - 2y = -4$, so $y = 3.5$, and the first gives $9 + 7 = 16$. A common wrong answer is 5, which comes from adding $16 + 4$ instead of $16 - 4$ and then dividing by 4. Another is 3.5, which is the value of $y$, not $x$. A third is 10, from subtracting the equations and mishandling signs. Add when the coefficients are opposites.