Question

Find the equation of straight line joining the point of intersection of 3x-y+9 = 0 and 2y +x -4 = 0 and the point of intersection of 2x+y = 4 and 2y = x +3.

Answer 1

3x-y+9 = 0 ------- (i)

2y +x -4 = 0 -------- (ii)

Solving equations (i) and (ii) we get,

x = -2, y = 3

2x+y = 4 -------- (iii)

2y = x +3 ------- (iv)

Solving equation (iii) and (iv) we get,

x=1 , y = 2

So, equation of line that passes through the given is

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

$\Rightarrow \frac{y-3}{2-3}=\frac{x-(-2)}{1-(-2)}$

$\Rightarrow \frac{y-3}{-1}=\frac{x-(-2)}{3}$

$\Rightarrow 3(y-3)=-(x+2)$

$\Rightarrow 3y-9=-x-2$

$\Rightarrow x+3y-7=0$