How many solutions does the system formed by x-y=3 and ay-ax=0 have for a nonzero number a?

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How many solutions does the system formed by x-y=3 and ay-ax=0 have for a nonzero number a?

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Answer 1 · 2016-12-04T07:13:55

We have no solution.

Explanation:

For a non-zero #a#, dividng both sides of the equation #ay-ax=0#, it becomes

#y-x=0#.

As #x-y=3#, we have the other equation as #y-x=-3#,

which means #-3=0#. But this is not possible.

Hence, we have no solution.

Note : In such cases, in Cartesian plane, the equations #x-y=3# and #ay-ax=0#, where #a!=0#, represent a pair of lines. As they do not meet, we have no solution.

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How many solutions does the system formed by x-y=3 and ay-ax=0 have for a nonzero number a?

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