Library / South African Mathematics Olympiad /19 of 48

South African Mathematics Olympiad

Algebra Difficulty 3.9 AMC 10/12 Find the answer South Africa

If $2x + 2y = 14$ and $x^2 - y^2 = 21$ then $x - y$ is equal to

Pick one

Solution

Since $2x + 2y = 14$ , we have $x + y = 7$ . Also since $x^2 - y^2 = (x + y)(x - y)$ , we have $7(x - y) = 21$ , so $x - y = 21/7 = 3$ .

Want a route through all this instead of an archive? The track puts 2,604 problems in a working order, from Junior Challenge level to the IMO shortlist.

Source: MathNet, licensed CC-BY-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project.