We have to solve
x + y = 5 ...(1)
x^2 + y^2 = 13 ...(2)
From (1) x = 5 - y
Substituting in (2)
(5 - y)^2 + y^2 = 13
=> 25 + y^2 - 10y + y^2 = 13
=> 2y^2 - 10y + 12 = 0
=> y^2 - 5y + 6 = 0
=> y^2 - 3y - 2y + 6 = 0
=> y(y - 3) - 2(y - 3) = 0
=> (y - 2)(y - 3) = 0
=> y = 2 and y = 3
x = 3 and 2
The solutions of the equations are (2, 3) and (3,2)
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