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

negative x plus y, equals negative 3 point 5, and, x plus 3 y, equals 9 point 5

If the ordered pair x comma y satisfies the system of equations above, what is the value of y ?

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Explanation

The correct answer is three halves. One method for solving the system of equations for y is to add corresponding sides of the two equations. Adding the left-hand sides gives open parenthesis, negative x plus y, close parenthesis, plus, open parenthesis, x plus 3 y, close parenthesis, or 4y. Adding the right-hand sides yields negative 3 point 5 plus 9 point 5, equals 6. It follows that 4 y equals 6. Finally, dividing both sides of 4 y equals 6 by 4 yields y equals six fourths or three halves. Note that 3/2 and 1.5 are examples of ways to enter a correct answer.