Maths Olympiad Prep

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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. Spacing and $ signs are ignored.

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

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