SOLUTION: Find points of intersection(x,y) of the following system of nonlinear equations. y=√x y=2x-6

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Question 1187062: Find points of intersection(x,y) of the following system of nonlinear equations.
y=√x
y=2x-6
Answer by greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!


We have two different expressions for y in terms of x; set them equal to each other and solve.

sqrt%28x%29=2x-6
x=4x%5E2-24x%2B36
x%5E2-25x%2B36=0
%284x-9%29%28x-4%29=0
x=9%2F4 or x=4

We squared both sides of the equation at one point, so we need to check for extraneous solutions.

(1) x = 9/4
y = sqrt(x) = 3/2
y = 2x-6 = 9/2-6 = -3/2

The two expressions for y evaluate differently; x = 9/4 is not a solution to the original equation.

(2) x = 4
y = sqrt(4) = 2
y = 2x-6 = 8-6 = 2

x=4 is a solution; it is the only solution.

ANSWER: (x,y) = (4,2) is the single intersection point.