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Given:

Lines 4x – 3y = 0 and 2x – 5y + 3 = 0 and parallel to 4x + 5 y + 6 = 0

To find:

The equation of a straight line through the point of intersection of the lines

Explanation:

The equation of the straight line passing through the points of intersection of 4x − 3y = 0 and 2x − 5y + 3 = 0 is given below:

4x − 3y + λ (2x − 5y + 3) = 0

⇒ (4 + 2λ)x + (− 3 − 5λ)y + 3λ = 0

⇒ y

The required line is parallel to 4x + 5y + 6 = 0 or, y
∴

⇒ λ

Hence, the required equation is

⇒ 28x + 35y – 48 = 0