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Algebra
/ Systems of two linear equations in two variables
Difficulty: Hard
The solution to the given system of equations is . What is the value of ?
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Explanation
The correct answer is . Subtracting the second equation in the given system from the first equation yields , which is equivalent to , or . Dividing each side of this equation by yields . Substituting for in the second equation yields . Adding to both sides of this equation yields .
Alternate approach: Multiplying each side of the second equation in the given system by yields . Subtracting the first equation in the given system from this equation yields , which is equivalent to , or . Dividing each side of this equation by yields .