Question

Prove that the following sets of three lines does not meet in a point.
$2x-3y=7,3x-4y=13$, and $3x-11y=33$.

Answer 1

$2x-3y=\mathrm{7......}\left(i\right)\Rightarrow x=\frac{7+3y}{2}3x-4y=\mathrm{13.......}\left(ii\right)3\left(\frac{7+3y}{2}\right)-4y=1321+9y-8y=26y+21=26\Rightarrow y=5x=\frac{7+3\left(5\right)}{2}\Rightarrow x=11$

So the point of intersection of $\left(i\right)$ and $\left(ii\right)$ is $(11,5)$

$3x-11y=\mathrm{33......}\left(iii\right)$

Substituting the point of intersection in $\left(iii\right)$

$3\left(11\right)-11\left(5\right)=33-55=-22-22\ne 33$

It does not satisfy the point of intersection , so they do not meet in a point