Answer :

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


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