Solve the system of equations algebraically x^2+y^2=100 x-y=2

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We have x^2 + y^2 = 100 and x - y = 2. We have to solve these equations for x and y.

x - y = 2

=> (x - y)^2 =2^2

=> x^2 + y^2 - 2xy = 4

substitute x^2 + y^2 = 100

=> 100 - 2xy = 4

=> 2xy = 96

=> xy = 48

substitute x = 2 + y

=> y(2 + y) = 48

=> y^2 + 2y - 48 = 0

=> y^2 + 8y - 6y - 48 = 0

=> y(y + 8) - 6(y + 8) = 0

=> (y - 6)(y + 8) = 0

=> y = 6 and y = -8

for y = 6, x = 8

for y = -8, x = -6

The required solution is (-6, -8) and (8, 6)

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