Find the equation of the line passing through the origin and the point of intersection of the lines 5x + 7y = 3 and 2x – 3y = 7.
Straight Line Eq
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Question

Find the equation of the line passing through the origin and the point of intersection of the lines 5x + 7y = 3 and 2x – 3y = 7.

KnowledgeBoat · Accepted Answer

⇒ 5x + 7y = 3 ….(1) ⇒ 2x - 3y = 7 ….(2) Multiplying equation (1) by 3, we get : ⇒ 3(5x + 7y) = 3.3 ⇒ 15x + 21y = 9 ….(3) Multiplying equation (2) by 7, we get : ⇒ 7(2x - 3y) = 7.7 ⇒ 14x - 21y = 49 ….(4) Adding equations (3) and (4) we get, ⇒ 15x + 21y + 14x - 21y = 9 + 49 ⇒ 29x = 58 ⇒ x = ⇒ x = 2. Substituting x = 2 in (1), we get : ⇒ 5(2) + 7y = 3 ⇒ 10 + 7y = 3 ⇒ 7y = 3 - 10 ⇒ 7y = -7 ⇒ y = ⇒ y = -1. Hence, the point of intersection of lines is (2, -1). The equation of the line joining (2, -1) and (0, 0) will be given by two-point form i.e., Substituting values in above equation we get, ⇒ y - (-1) = (x - 2) ⇒ y + 1 = (x - 2) ⇒ -2(y + 1) = (x - 2) ⇒ -2y - 2 = x - 2 ⇒ x + 2y - 2 + 2 = 0 ⇒ x + 2y = 0. Hence, equation of line is x + 2y = 0.

Mathematics

Find the equation of the line passing through the origin and the point of intersection of the lines 5x + 7y = 3 and 2x – 3y = 7.

Straight Line Eq

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Find the equation of the line passing through the origin and the point of intersection of the lines 5x + 7y = 3 and 2x – 3y = 7.

Straight Line Eq

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