Find the equation of the line passing through the intersection of the

1.	Find the equation of the line passing through the intersection of the lines 2x − y + 5 = 0 and x + y + 1 = 0 and the origin.
Answer» It, the required line is of the form (2x − y + 5 = 0) + λ (x + y + 1) = 0 Since this also passes through (0, 0), we have λ = −5. Hence the required line is (2x − y + 5) − 5 (x + y + 1) = 0 -3x - 6y = 0 x + 2y = 0 Direct Method: Solving the equations 2x − y + 5 = 0 and x + y + 1 = 0, we get the point of intersection (−2, 1). Therefore, the equation of the line joining (−2, 1) and (0,0) is y = 0 -1/0 + 2 x or x + 2y = 0

Find the equation of the line passing through the intersection of the lines 2x − y + 5 = 0 and x + y + 1 = 0 and the origin.

Answer»

It, the required line is of the form

(2x − y + 5 = 0) + λ (x + y + 1) = 0

Since this also passes through (0, 0), we have λ = −5.

Hence the required line is

(2x − y + 5) − 5 (x + y + 1) = 0

-3x - 6y = 0

x + 2y = 0

Direct Method:

Solving the equations 2x − y + 5 = 0 and x + y + 1 = 0,

we get the point of intersection (−2, 1). Therefore, the equation of the line joining (−2, 1) and (0,0) is

y = 0 -1/0 + 2 x

or x + 2y = 0

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Find the equation of the line passing through the intersection of the lines 2x − y + 5 = 0 and x + y + 1 = 0 and the origin.

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