In all the following systems of equations determine whether the system has a unique solution, no solution or infinite solutions. If In case there is a unique solution$x-3y-3=0$, $3x-9y-2=0$
In all the following systems of equations determine whether the system has a unique solution, no solution or infinite solutions. If In case there is a unique solution$x-3y-3=0$, $3x-9y-2=0$

Given system of equations is:

$x-3y-3=0$

$3x-9y-2=0$

Above equations are in the form of

${{a}_{1}}x+{{b}_{1}}y-{{c}_{1}}=0$

${{a}_{2}}x+{{b}_{2}}y-{{c}_{2}}=0$

Here, ${{a}_{1}}=1,{{b}_{1}}=-3,{{c}_{1}}=-3$

${{a}_{2}}=3,{{b}_{2}}=-9,{{c}_{2}}=-2$

So according to the question, we get

${{a}_{1}}/{{a}_{2}}=1/3$

${{b}_{1}}/{{b}_{2}}=-3/-9=1/3$

${{c}_{1}}/{{c}_{2}}=-3/-2=3/2$

${{a}_{1}}/{{a}_{2}}={{b}_{1}}/{{b}_{2}}\ne {{c}_{1}}/{{c}_{2}}$

Therefore, we can conclude that, given system of equation has no solution.