Explanation

Know your common quadratics. You are asked for the value of x + y.

Because \(x^2 - y^2 =(x + y)(x - y) = 24\), if the value of (x − y) is found, (x + y) can be figured out.

Manipulate the equation 0.5(y − x) = –1 to get (y − x) = –2.

Multiplying both sides by –1, you get x – y = 2.

Substitute this value into the equation (x + y)(x – y) = 24 and then divide both sides of the equation by 2 to get (x + y) = 12. The answer is choice (D).
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