Alvin’s first step in solving the given system of equations is to multiply the first equation by 2 and the second equation by –3. Which linear combination of Alvin’s system of equations reveals the number of solutions to the system?9x + 4y = 366x + 2.5y = 24

Multiply the first equation by 2 to get 18x + 8y = 72, and the second by −3 to get −18x − 7.5y = −72. Adding these equations cancels the x-terms and gives 0x + 0.5y = 0, matching choice C. This gives y = 0; substituting into either original equation determines a single value of x, so the system has one solution.

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