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Systems of two linear equations in two variables SAT question

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

$6 x + 7 y = 28$
$2 x + 2 y = 10$

The solution to the given system of equations is $(x, y)$ . What is the value of y?

ExplanationShow

Choice A is correct. The given system of linear equations can be solved by the elimination method. Multiplying each side of the second equation in the given system by $3$ yields $(2 x + 2 y) (3) = (10) (3)$ , or $6 x + 6 y = 30$ . Subtracting this equation from the first equation in the given system yields $(6 x + 7 y) - (6 x + 6 y) = (28) - (30)$ , which is equivalent to $(6 x - 6 x) + (7 y - 6 y) = 28 - 30$ , or $y = - 2$ .

Choice B is incorrect. This is the value of $x$ , not the value of $y$ .

Choice C is incorrect and may result from conceptual or calculation errors.

Choice D is incorrect and may result from conceptual or calculation errors.

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Systems of two linear equations in two variables SAT question

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