Question

Find the equation of the line passing through the point of intersection of the line 4x +3y+2=0 and 6x+5y+6=0 and the point of intersection of the lines 4x–3y–17=0 and 2x+3y+5=0.​

Answer 1

The equation of line is 2x + 3y = 0 .

Point of intersection of line  4x +3y+2=0 and 6x+5y+6=0 .

We get , point ( 4 , -6 ).

Also , Point of intersection of line 4x–3y–17=0 and 2x+3y+5=0 .​

We get , point ( 2 , -3 ).

Equation of line passing through two point is :

$y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)\\\\y-(-3)=\dfrac{-6-(-3)}{4-2}(x-2)\\\\y+3=\dfrac{-3}{2}(x-2)\\\\2y+3x=0$

Hence, this is the required solution.

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Coordinate Geometry

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