Maths Olympiad Prep

Library / /15 of 353

Algebra Difficulty 4.4 AIME Find the answer

If x+2y3z=7x+2 y-3 z=7 and 2xy+2z=62 x-y+2 z=6, determine 8x+y8 x+y.

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Solution

8x+y=2(x+2y3z)+3(2xy+2z)=2(7)+3(6)=328 x+y=2(x+2 y-3 z)+3(2 x-y+2 z)=2(7)+3(6)=32

Want a route through all this instead of an archive? The track puts 2,000 problems in a working order, from AMC 10 level to the IMO shortlist.

Source: Omni-MATH, licensed Apache-2.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project.