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Algebra
/ Systems of two linear equations in two variables
Difficulty: Medium
The solution to the given system of equations is . What is the value of ?
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Explanation
Choice C is correct. It's given by the first equation in the system that . Substituting for in the second equation in the system yields . Multiplying the left-hand side of this equation by and the right-hand side by yields . Adding to both sides of this equation yields . Multiplying both sides of this equation by yields .
Choice A is incorrect and may result from conceptual or calculation errors.
Choice B is incorrect and may result from conceptual or calculation errors.
Choice D is incorrect and may result from conceptual or calculation errors.