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

Dec 4, 2016

We have no solution.

Explanation:

For a non-zero $a$, dividng both sides of the equation $a y - a x = 0$, 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 $a y - a x = 0$, where $a \ne 0$, represent a pair of lines. As they do not meet, we have no solution.