Question

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

Answer 1

intercept form
x/a+y/b=1
x/-4+y/b=1
by solving this we get
bx-4y/-4b=1
bx-4y=-4b
this is equation 1
now we find the value of X and y from the given to equation
2x+3y=0
(x-5y=7)2
2x-10y=14


13y=-14
y=-14/13
x=
then put value of X and y in equation 1 we will get the final eqation

Answer 2

Solution :

Equation of the required line can be given as

2x+3y−4+k(x−5y−7)=0

(2+k)x+(3−5k)y−(4+7k)=0→(1)

As, x- intercept is given, we can put y=0

∴(2+k)x=4+7k

⇒(2+k)(−4)=4+7k

⇒−8−4k=4+7k⇒k=−1211

So, putting value of k in (1), we get the required equation.

(2−1211)x+(3+6011)−(4−8411)=0

⇒10x+93y+40=0, which is the required equation.