Question

Find the equation of the line through the intersection of the lines 2x+3y-4=0and x-5y+7=0has x intercept equal to -4

Answer 1

Heya!!

Equation of a line passing through the intersection of two lines is given by

A1 + k A2 = 0

Where A1 = 2x + 3y - 4 ,A2 = x - 5y + 7

And k belongs to Any real number.

( 2x + 3y - 4 )+ k ( x - 5y + 7 ) = 0

x ( 2 + k ) + y ( 3 - 5k ) + 7k - 4 = 0

Now, it is given that this line passes through the point ( -4 , 0 ).

i,e x = - 4 And y = 0

-4 ( 2 + k ) + 7k - 4 = 0

3k - 12 = 0

3k = 12

k = 4

Now, put value of k in above equation to get required Equation of line passing through the intersection of other two lines.

x ( 2 + 4 ) + y ( 3 - 20 ) + 24 = 0

6x - 17y + 24 = 0