Question 65805This question is from textbook An Incremental Development
: Solve
x^2 + y^2 = 25
x - y = 1
This question is from textbook An Incremental Development
Answer by uma(370)   (Show Source):
You can put this solution on YOUR website! x^2 + y^2 = 25------------(1)
x - y = 1
==> x = y+1
Plugging in this value in (1),
(y+1)^2 + y^2 = 25
==> y^2 + 2y + 1 + y^2 = 25
==> 2y^2 + 2y + 1 - 25 = 0
==> 2y^2 + 2y - 24 = 0
==> y^2 + y - 12 = 0 [dividing by 2 throughout]
==> y^2 + 4y - 3y - 12 = 0
==> y(y+4) - 3(y+4) = 0
==> (y+4)(y-3) = 0
==> y+4 = 0 or y - 3 = 0
==> y = -4 or y = 3
==> x = -4+1 or x = 3+1
==> x = -3 or x = 4
Thus x = -3 and y = -4 and x = 4 and y = 3 are the two sets of solutions.
Good luck!!!
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