Question 1108061
1) 2x/3 + y/6 = 1
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2) x/6 - y/2 = 1
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rewrite equations 1 and 2 using the least common multiple of the divisors
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3) 4x + y = 6
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4) x - 3y = 6
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multiply equation 3 by 3
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5) 12x + 3y = 18
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add equation 5 and equation 4
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13x = 24
x = 24/13
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use equation 2 to solve for y
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(24/13) * (1/6) - y/2 = 1 
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(4/13) - y/2 = 1
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-y/2 = 9/13
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y = -18/13
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x = 24/13 and y = -18/13
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check answer with equation 1
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(2/3) * (24/13) + (1/6) * (-18/13) = 1
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(16/13) - (3/13) = 1
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1 = 1
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check answer in equation 2
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(1/6) * (24/13) - (1/2) * (-18/13) = 1
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(4/13) + (9/13) = 1
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1 = 1
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answer checks
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