Mathematics - Straight Lines Question with Solution | TestHub

If $\frac{a_i}{c_i}=\lambda$ for all $i$, each line is $(\lambda x+1)c_i+b_{i}y=0$ and all pass through $\left(-\frac{1}{\lambda },0\right)$. So they are concurrent. The points $\left(\frac{a_i}{c_i},\frac{b_i}{c_i}\right)$ are collinear exactly when the determinant of the coefficients $a_i,b_i,c_i$ is zero, which is the condition of concurrency, and the case $\frac{a_i}{c_i}$ equal puts all three points on a line parallel to the $y$-axis. Both statements are true and Statement 2 explains Statement 1.