Question

Find the equation of the line joining the point (3, 5) to the point of intersection of the lines $4x+y-1=0and7x-3y-35=0.$

Answer 1

$\text{The point of intersection of the lines}$

$4x+y-1=0and7x-3y-35=0is$

$y=1-4x$

$7x-3(1-4x)-35=0$

$7x-3+12x-35=0$

$19x-38$

$x=2$

$\Rightarrow y=1-4x=1-8=-7$

$\therefore LetP(2,-7)andQ(3,5)$

$\text{The equation of line PQ is}$

$y-y_1=m(x-x_1)$

$y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$

$y-(-7)=\frac{5-(-7)}{3-2}(x-2)$

$y+7=12(x-2)$

$y=12x=-31$

$12x-y-31=0$