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Algebra / Systems of two linear equations in two variables Difficulty: Medium

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?

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Explanation

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 2x+2y(3)=103, or 6x+6y=30. Subtracting this equation from the first equation in the given system yields 6x+7y-6x+6y=28-30, which is equivalent to 6x-6x+7y-6y=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.