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a+b^2 = x+y^2 and a^2 +b = x^2 +y, if a+b+x+y < 2

Source: 1995 Swedish Mathematical Competition p3

April 2, 2021
algebrasystem of equationsSystem

Problem Statement

Let a,b,x,ya,b,x,y be positive numbers with a+b+x+y<2a+b+x+y < 2. Given that {a+b2=x+y2a2+b=x2+y\begin{cases} a+b^2 = x+y^2 \\ a^2 +b = x^2 +y\end {cases} show that a=xa = x and b=yb = y
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