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Algebra 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.