ShmoopTube

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Here's your shmoop du jour:

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Solve for a. 3a + 16b = 42 6a + 20b = 12

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And here are the potential answers...

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Alright. it's really checking whether we realize that we can ADD equations.

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But if we just add the two equations above, it doesn't really do anything for us -- so

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what we really want to do is add them in such a way so that we GET RID OF a variable.

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If we just have ONE variable, the problem is a whole lot easier to solve.

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Okay, let's set our sights on crushing a.

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We can start by multiplying both sides of the first equation by... negative 2.

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Then, when we add the two equations, we'll have no a and a whole lotta b.

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So here we go.

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Negative 2 times 3a plus 16b equals 42... which gets us negative 6a minus 32b equals negative 84.

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Now we just add the two equations; our a's cancel out... negative 32b plus 20b is negative

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12b, and negative 84 plus 12 is negative 72.

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Multiply both sides by negative 1 and we have 12b equals 72.

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Divide both sides by 12 and we have b equals 6.

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We can now just plug in 6 for b, and 6a plus 120 equals 12.

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Subtract 120 from both sides and we get 6a equals negative 108; divide both sides by

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6 and we get a equals negative 18.

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The answer is A.

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