Question 701104: How do I solve this set of simulataneous equation?
xy+20=5x
x-2y-3=0
Answer by DrBeeee(684)   (Show Source):
You can put this solution on YOUR website! Normally you can't because of the nonlinear term x*y, but in this case you can get the solution by substitution.
Given
(1) xy + 20 = 5x and
(2) x - 2y -3 = 0
Solve (2) for y
yields
(3) y = (x-3)/2
Put this y into (1) and get
(4) x(x-3)/2 + 20 = 5x or
(5) x^2 - 3x + 40 = 10x or
(6) x^2 - 13x + 40 = 0
which factors to
(7) (x-5)*(x-8) = 0
which has roots for x
(8) x = {5,8}
Put each value of x into (2) and get the corresponding values of y
(9) y = {1,5/2} or the solution points
(10) (5,1) and (8,5/2)
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