Day 2: Two Simultaneous Equations

Algebra Level 3

Find the value of y 2 y^2 where: 2 x + y = 20 x 2 + x y = 47 2x+y=20\\x^2+xy=47


This problem is part of the Advent Calendar 2015 .


The answer is 212.

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1 solution

Michael Ng
Dec 3, 2015

Squaring the first equation gives 4 x 2 + 4 x y + y 2 = 4 ( x 2 + x y ) + y 2 = 4 × 47 + y 2 = 400 4x^2+4xy+y^2=4(x^2+xy) +y^2 = 4 \times 47 +y^2 = 400 .

Therefore y 2 = 212 y^2=\boxed{212} . However for a complete solution we must show that this does yield a solution; substituting our value of y y works perfectly.

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