If x² + y = 10 and x² - y = 4, what is the value of y?

The $y$-terms have opposite signs, so subtract the second equation from the first: $(x^2 + y) - (x^2 - y) = 10 - 4$, giving $2y = 6$ and $y = 3$. Then $x^2 = 7$, so $x = \pm\sqrt{7}$. Check: $7 + 3 = 10$ and $7 - 3 = 4$. A common wrong answer is 7, which is the value of $x^2$, not $y$. Another is 6, which comes from forgetting to divide by 2 after elimination, and a third is 14, from adding the equations and getting $2x^2 = 14$, which solves for a different quantity. Make sure you report the variable the question asks for.