What is the solution (a, b) to this system of linear equations?3a+6b=452a-2b=-12

Divide the first equation, 3a + 6b = 45, by 3 to get a + 2b = 15. Divide the second equation, 2a − 2b = −12, by 2 to get a − b = −6. Subtract the second simplified equation from the first: 3b = 21, so b = 7; then a − 7 = −6 gives a = 1. The solution is (1, 7), choice C.

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