Question 1187062
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We have two different expressions for y in terms of x; set them equal to each other and solve.<br>
{{{sqrt(x)=2x-6}}}
{{{x=4x^2-24x+36}}}
{{{x^2-25x+36=0}}}
{{{(4x-9)(x-4)=0}}}
{{{x=9/4}}}  or  {{{x=4}}}<br>
We squared both sides of the equation at one point, so we need to check for extraneous solutions.<br>
(1) x = 9/4
y = sqrt(x) = 3/2
y = 2x-6 = 9/2-6 = -3/2<br>
The two expressions for y evaluate differently; x = 9/4 is not a solution to the original equation.<br>
(2) x = 4
y = sqrt(4) = 2
y = 2x-6 = 8-6 = 2<br>
x=4 is a solution; it is the only solution.<br>
ANSWER: (x,y) = (4,2) is the single intersection point.<br>