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VITEEE 2010 Paper

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Question : 97 of 120

Marks: +1, -0

The equation of straight line through the intersection of line 2x + y = 1 and 3x + 2y = 5 and passing through the origin is

7x + 3y = 0
7x - y = 0
3x + 2y = 0
x + y = 0

Solution:

Let

\;L_{1}=2x+y-1=0

L_{2}=3x+2y-5=0

The equation of straight line passing through the intersection point of the line

L_{1}\text{ and }L_{2}

is gven by

L_{1}+\lambda L_{2}=0

⇒

(2x+y-1)+\lambda(3x+2y-5)=0

Since, this line passes through the origin also

(0+0-1)+\lambda(0+0-5)=0

⇒

-5\lambda=1\Rightarrow \lambda=-\frac{1}{5}

Required line is

(2x+y-1)-\frac{1}{5}(3x+2y-5)=0

⇒

\left(2-\frac{3}{5}\right)x+\left(1-\frac{2}{5}\right)y-1+1=0

⇒

\frac{7}{5}x+\frac{3}{5}y=0\Rightarrow 7x+3y=0

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