If $3 a-2 b+5 c=0$, the family of lines $a x+b y+c=0$ are always concurrent at a point whose coordin

Question

If $3 a-2 b+5 c=0$, the family of lines $a x+b y+c=0$ are always concurrent at a point whose coordinates are

Professor PC Thomas Classes · Answer

$c = -\frac{3}{5}a + \frac{2}{5}b$. Substituting into line eq: $a(x-3/5) + b(y+2/5) = 0 \Rightarrow (3/5, -2/5)$. [FLAG: matching signs]