06/07/2020 (2011: National Sprint Round, Problem 20)

Q: If  x/2 + y/3 = 1 and x/4 + 2y/3 = -1, what is the value of the sum of x and y?

A: 1

This is a system of equations, so we can use elimination and multiply the second equation by 2 to get:

x/2 + 4y/3 = -2 and subtract it from x/2 + y/3 = 1 -->

y/3 - 4y/3 = 1 - (-2) -->

-3y/3 = 3 -->

-y = 3 -->

y = -3

Plug In y = -3 to find x

x/2 + -3/3 = 1 -->

x/2 - 1 = 1 -->

x/2 = 2 -->

x = 4

We add the values of x any y together:

4 + (-3) = 1.