# Find the equation of the straight line passing through the point of intersection of 2x + 3y + 1 = 0 and 3x – 5y – 5 = 0 and equally inclined to the axes.

Given:

2x + 3y + 1 = 0 and 3x – 5y – 5 = 0

To find:

The equation of the straight line passing through the point of intersection of 2x + 3y + 1 = 0 and 3x – 5y – 5 = 0 and equally inclined to the axes.

Explanation:

The equation of the straight line passing through the points of intersection of 2x + 3y + 1 = 0 and 3x 5y 5 = 0 is

2x + 3y + 1 + λ(3x 5y 5) = 0

(2 + 3λ)x + (3 5λ)y + 1 5λ = 0
y

The required line is equally inclined to the axes. So, the slope of the required line is either 1 or 1.

and

-2 – 3λ = 3 – 5λ and 2 + 3λ = 3 – 5λ

λ and

Substituting the values of λ in (2 + 3λ)x + (3 5λ)y + 1 5λ = 0, we get the equations of the required lines.

19x – 19y – 23 = 0 and 19x + 19y + 3 = 0

Hence, required equation is 19x – 19y – 23 = 0 and 19x + 19y + 3 = 0

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