Math CentralQuandaries & Queries


Question from ryan, a student:

3         4
--   -    --      =     1      (1)
x         y

7       2             11
--   -  --        =   --       (2)
x       y              12


When you have simultaneous equations in two variables, the general strategy is to is to get rid of one of the variables, leaving you with one equation in one variable. The easiest way to proceed might be to multiply your second equation by -2, then add the two equations.

If you do not like working with fractions, then it is easy to get rid of them here: just set u = 1/x and v = 1/y. Next, solve for u and v the usual way you were taught to solve simultaneous equations. After you have found u and v, then x will be 1/u and y will be 1/v.



Hi Ryan.

To get this solution started, why not multiply the second equation by 2, then subtract it from the first equation? That way you can eliminate the y terms and find x.

Write back if you need more help.
Stephen La Rocque

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