How do you solve (12)x−(13)y=−3 and (18)x+(16)y=0?

1 Answer
José F.
Jan 18, 2016

(x,y)=(−4,3)

Explanation:

(12)x−(13)y=−3 and (18)x+(16)y=0

The minimum common multiple between 2,3,6 and 8 is 24. So
let's convert all these fractions in something/24:

(1224)x−(824)y=−(7224) and (324)x+(424)y=0

Then multiply all the equalities by 24:

12x−8y=−72 and 3x+4y=0

If 3x+4y=0 the double 6x+8y is also 0, so we can
add it to the other equation without change the result:

6x+8y=0 plus 12x−8y=−72 gives 18x=−72

So, x=−7218=−4

and applying the value x=−4 to the expression:

3x+4y=0

gives

3⋅(−4)+4y=0
4y=12
y=3

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