SOLUTION: Solve the following equation: 4ax + by = 11ab 8ax - 5by = ab

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Question 126294: Solve the following equation:
4ax + by = 11ab
8ax - 5by = ab
Answer by HyperBrain(694) About Me  (Show Source):
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(1)4ax + by = 11ab
(2)8ax - 5by = ab
FRom(1),
4ax + by = 11ab
4ax+by-by=11ab-by
4ax=11ab-by
(3)x=%2811ab-by%29%2F4a
Substituting (3) to (2),
8a%28%2811ab-by%29%2F4a%29+-+5by+=+ab
2(11ab-by)-5by=ab
22ab-2by-by=ab
22ab-3by=ab
-3by=ab-22ab
-3by=-21ab
3by=21ab
by=7ab
y=7a
Solving for x,
x=%2811ab-by%29%2F4a
x=%2811ab-b%287a%29%29%2F4a
x=%2811ab-7ab%29%2F4a
x=4ab%2F4a
x=b
Thus, the system is true if x=b and y=4a.

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