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Question

Given, y=x and (y2)24=x
The system of equations above intersects at two points. Find the sum of the x and y co-ordinates of the point of intersection of the pair of equations in Quadrant 1.

A
4
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B
5
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C
6
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D
7
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Solution

The correct option is C 6
Substitute x for y in the second equation to get (x2)24=x.
Expand the left side of the equation to get (x2)(x2)4=x or x24x+44=x.
Simplify the equation to get x24x=x.
Set the equation to 0 to get x23x=0.
Factor an x out of the equation to get x(x3)=0.
Therefore, either x=0orx3=0 and x=3.
According to the question, the point of intersection is in quadrant I, where the x and y values are both positive.
Therefore, x=3 and y=3.
The sum of 3+3=6.
The correct answer is 6.

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