Given the equations below, what is the value of a + b?

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Accepted Answer

First, simplify the first equation by multiplying (a + 3) by 1 ⁄ 2 . The first equation becomes 1 ⁄ 2 a + 3 ⁄ 2 – b = –6. Subtract 3 ⁄ 2 from both sides, and the equation becomes 1 ⁄ 2 a – b = – 15 ⁄ 2 . Then, multiply the equation by –6 and add it to the second equation. The a terms will drop out, and you can solve for b: –6( 1 ⁄ 2 a – b = – 15 ⁄ 2 ) = –3a + 6b = 45 –3a + 6b = 45 + 3a – 2b = –5 4b = 40 b = 10 Substitute the value of b into the second equation and solve for a: 3a – 2(10) = –5 3a – 20 = –5 3a = 15 a = 5 Since a = 5 and b = 10, the value of a + b = 5 + 10 = 15.

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