Solve 7x-4y=8?

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2 Answers
David Drayer
Aug 7, 2018

As this is an equation with two variables there are an infinite number of possible solutions.

Explanation:

for example x = 1 y = -1/4

or x = 0 y = -2

F. Javier B.
Aug 14, 2018

See below

Explanation:

We can consider equation above as a Diofantic equation #Ax-By=C#

A diofantic equation is a particular case of general equation where solutions are allways integers

We consider by now the homogeneus case

#7x-4y=0#. The general solution of this equation is #x=4t# and #y=7t# with #t# an integer parameter (infinite solutions)

Now the complete case solutions are obtained

#x=x_0+4t#
#y=y_0+7t#

where #x_0, y_0# are paticular solutions of homegeneus case

The solution is unique if and only if GCD(A,B) divide to C

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