Question

Find the equation of the line passes through the point (2,3) and the point of 

intersection of the line 3𝑥 + 2𝑦 = 2 and 4𝑥 + 3𝑦 = 7 meet.

Answer 1

L₁=3x+2y-2=0

L₂=4x+3y-7=0

P=(2,3)

Find the intersection point of L₁ and L₂

$x=(\frac{(-2*3)-(2*-7)}{(2*4)-(3*3)})$

$x=\frac{8}{-1}=-8$

3(-8)+2y=2

2y=2+24

y=13

Q=(-8,13)

Equation of QP will be given by;

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

$y-13=\frac{3-13}{2+8}(x+8)$

$y-13=-1(x+8)$

$y-13=-x-8$

$x+y-13+8=0$

$x+y-5=0$ Is the equation of the line.