Question

Find the equation to the straight line passing through. the point $(3,2)$ and the point intersection of the line $2x+3y=1$ and $3x-4y=6$.

Answer 1

Equation of lines is given as

$2x+3y=1⟶\left(1\right)3x-4y=6⟶\left(2\right)$

solving (1) and (2) we get,

$x=\frac{22}{17}andy=\frac{-9}{17}$

therefore point of intersection is $(\frac{22}{17},\frac{-9}{17})$

hence the equation of the straight line passes through the point $(3,2)$ and point of intersection of lines is given as;

$\frac{y-2}{\frac{-9}{17}-2}=\frac{x-3}{\frac{22}{17}-3}\Rightarrow 43x-29y=71$