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

y equals, 2 x minus 3, and, 3 y equals 5 x

In the solution to the system of equations above, what is the value of y ?

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Explanation

Choice D is correct. Multiplying both sides of y equals 2 x minus 3 by 5 results in 5 y, equals 10 x minus 15. Multiplying both sides of 3 y, equals 5 x by 2 results in 6 y, equals 10 x. Subtracting the resulting equations yields 5 y minus 6 y, equals, open parenthesis, 10 x minus 15, close parenthesis, minus, 10 x, which simplifies to negative y equals negative 15. Dividing both sides of negative y equals negative 15 by negative 1 results in y equals 15.

Choices A and B are incorrect and may result from incorrectly subtracting the transformed equation. Choice C is incorrect and may result from finding the value of x instead of the value of y.