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Advanced Math
/ Nonlinear equations in one variable and systems of equations in two variables
Difficulty: Medium
If one solution to the system of equations above is 
, what is one possible value of x ?
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Explanation
The correct answer is either 8 or 9. The first equation can be rewritten as 
. Substituting 
for y in the second equation gives 
. By applying the distributive property, this can be rewritten as 
. Subtracting 72 from both sides of the equation yields 
. Factoring the left-hand side of this equation yields 
. Applying the Zero Product Property, it follows that 
and 
. Solving each equation for x yields 
and 
respectively. Note that 8 and 9 are examples of ways to enter a correct answer.