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Question
Find the equation of the lines passing through the point of intersection lines 4x − y + 3 = 0 and 5x + 2y + 7 = 0, and parallel to x − y + 5 = 0
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Solution
The equation of the straight line passing through the point of intersection of the lines.
4x – y + 3 = 0 and 5x + 2y + 7 = 0 is
(4x – y + 3) + λ(5x + 2y + 7) = 0 ......(1)
Equation of a line parallel to x – y + 5 = 0 will be of the form x – y + k = 0.
It passes through (–1, –1)
⇒ – 1 + 1 + k = 0
⇒ k = 0.
So the required line is x – y = 0 ⇒ x = y.
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