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Advanced Math
/ Nonlinear equations in one variable and systems of equations in two variables
Difficulty: Hard
In the xy-plane, the graph of 
intersects the graph of 
at the points 
and 
. What is the value of a ?
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Explanation
The correct answer is 5. The intersection points of the graphs of and can be found by solving the system consisting of these two equations. To solve the system, substitute x for y in the first equation. This gives 
. Subtracting x from both sides of the equation gives 
. Factoring 
out of each term on the left-hand side of the equation gives 
. Therefore, the possible values for x are 0 and 5. Since , the two intersection points are 
and 
. Therefore, 
.