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Algebra
/ Systems of two linear equations in two variables
Difficulty: Medium
In the xy-plane, the graph of 
intersects the graph of 
at the point 
. What is the value of a ?
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Explanation
Choice C is correct. Since the graph of intersects the graph of at the point , the ordered pair is the solution to the system of linear equations consisting of and , and the value of a is the value of x in the solution of this system. Since both 
and 
are equal to y, it follows that 
. Subtracting x from and adding 6 to both sides of the equation yields 
. Therefore, the value of a is 9.
Choices A and B are incorrect and may result from a calculation or conceptual error in solving the system of equations consisting of and . Choice D is incorrect. This is the value of b, not a.