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Algebra
/ Systems of two linear equations in two variables
Difficulty: Hard
In the given system of equations, and are constants. The system has infinitely many solutions. What is the value of ?
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Explanation
The correct answer is . It’s given that the system has infinitely many solutions. A system of two linear equations has infinitely many solutions if and only if the two linear equations are equivalent. Multiplying each side of the first equation in the system by yields , or . Since this equation is equivalent to the second equation and has the same right side as the second equation, the coefficients of and , respectively, should also be the same. It follows that and . Therefore, the value of is , or . Note that 2/7, .2857, 0.285, and 0.286 are examples of ways to enter a correct answer.