If x² + y = 21 and x² - y = 11, what is the positive value of x?

Add the two equations to eliminate $y$: $(x^2 + y) + (x^2 - y) = 21 + 11$, so $2x^2 = 32$ and $x^2 = 16$. Then $x = \pm 4$, and the positive value is 4. Check: $y = 21 - 16 = 5$, and $16 - 5 = 11$. A common wrong answer is 16, which is $x^2$, not $x$. Another is 5, which is the value of $y$, and a third is $\sqrt{32} \approx 5.66$, which results from forgetting to divide by 2 before taking the square root. Make sure you solve for the variable asked.