Math CentralQuandaries & Queries


Question from Rohan, a student:

x-2/3 + y - 1/4 = 13/12
2-x/2 + 3 + y/3 = 11/6

Hi Rohan,

The way you have written the first equation it is

\[x - \frac23 + y - \frac14 = \frac{13}{12}\]

but I think you might mean

\[\frac{x-2}{3} + \frac{y-1}{4} = \frac{13}{12}.\]

You need to use parentheses to make it clear.

In any case the denominators are 3, 4 and 12 and the least common multiple of 3, 4 and 12 is 12. I suggest you multiply both sides of the equation by 12 and simplify. This will give you an equation with integer coefficients. Apply a similar technique to the second equation and then solve the two resulting equations.


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