Question

Find the equation of line passing through the point of intersection of lines 5x +7y-3=0 and 2x-3y-7=0

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Answer 1

Solution:-At the point of intersection,they coordinates of both the lines will be common

Let the third required line be ax+by+c

so first let us take it out

5x+7y-3=0........i)

2x-3y-7=0.......ii)

multiply the second equation by 5 and first by 2

10x+14y=6......iii)

10x-15y=35.....iv)

subtract iv) by iii)

29y=-29

y=-1

put this equation in i)

5x=10

x=2

this shows that there is a coordinate(2,-1) with which both lines are passing,,

also,.it passes.to the third,required line

putting the value of x and y in eqaution of required line we get

2a-b+c=0

c=b-2a

so, the required line will be

ax+by +(b-2a)=0

{hope it helps you}