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Systems of two linear equations in two variables SAT question

Math · Algebra · Medium · Answer it here, explanation included.

In the xy-plane, the graph of $y equals, x plus 3$ intersects the graph of $y equals, 2 x minus 6$ at the point $with coordinates a, comma b$ . What is the value of a ?

ExplanationShow

Choice C is correct. Since the graph of $y equals, x plus 3$ intersects the graph of $y equals, 2 x minus 6$ at the point $with coordinates a, comma b$ , the ordered pair $a, comma b$ is the solution to the system of linear equations consisting of $y equals, x plus 3$ and $y equals, 2 x minus 6$ , and the value of a is the value of x in the solution of this system. Since both $x plus 3$ and $2 x minus 6$ are equal to y, it follows that $x plus 3, equals, 2 x minus 6$ . Subtracting x from and adding 6 to both sides of the equation yields $9 equals x$ . 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 $y equals, x plus 3$ and $y equals, 2 x minus 6$ . Choice D is incorrect. This is the value of b, not a.

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Systems of two linear equations in two variables SAT question

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