Suppose that [imath]\ell_1~\&~\ell_2[/imath] are two lines represented by the general linear equation [imath]Ax+By+C=0[/imath]
Can you explain the following? From the given there must be a point [imath](p,q)[/imath]. on one of lines but not the other.
Say it is is on [imath]\ell_1[/imath]. Because [imath]Ax+By+C=0[/imath] determines [imath]\ell_1[/imath] we have [imath]Ap+Bq+C=0[/imath], WHY?
Now can you explain why [imath](p,q)\notin\ell_2\text{ means that }Ap+Bq+C\ne 0~?[/imath]
Please reply with what you are able to do.
[imath][/imath][imath][/imath][imath][/imath] [imath][/imath][imath][/imath][imath][/imath]