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Question
Answer the following question:
Find the equation of the line which passes through the point of intersection of lines x + y − 3 = 0, 2x − y + 1 = 0 and which is parallel X-axis
Solution
Since the required line passes through the point of intersection of x + y − 3 = 0 and 2x − y + 1 = 0, its equation is of the form.
(x + y − 3) + k(2x − y + 1) = 0 ...(1)
i.e., (1 + 2k)x + (1 − k)y − (−3 + k) = 0
Slope of this line = `(-(1 + 2"k"))/(1 - "k")`
Since it is parallel to X-axis, its slope = 0
∴ `(-(1 + 2"k"))/(1 - "k")` = 0
∴ 1 + 2k = 0
∴ k = `-1/2`
Substituting k = `(-1)/2` in (1), we get
`(x + y - 3) + ((-1)/2) (2x - y + 1)` = 0
∴ 2x + 2y − 6 − 2x + y − 1 = 0
∴ 3y − 7 = 0
This is the equation of required line.
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