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Systems of two linear equations in two variables SAT question

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

one half y equals 4
x minus, one half y, equals 2

The system of equations above has solution (x, y). What is the value of x ?

ExplanationShow

Choice D is correct. Adding the corresponding sides of the two equations eliminates y and yields x equals 6, as shown.

The equation one half y equals 4, added to the equation x minus one half y, equals 2, gives the equation x plus 0, equals 6

If (x, y) is a solution to the system, then (x, y) satisfies both equations in the system and any equation derived from them. Therefore, x equals 6.

Choices A, B, and C are incorrect and may be the result of errors when solving the system.

 

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