System solving Solve the system x+y=5 x^2+y^2=13

Expert Answers

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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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