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Question
Find the equation of the line parallel to the X-axis and passing through the point of intersection of lines x + y − 2 = 0 and 4x + 3y = 10
Solution
Since the required line passes through the point of intersection of x + y − 2 = 0 and 4x + 3y = 10, its equation is of the form.
(x + y − 2) + k(4x + 3y − 10) = 0 ...(1)
i.e., (1 + 4k)x + (1 + 3k)y + (−2 − 10k) = 0
Slope of this line = `(-(1 + 4"k"))/(1 + 3"k")`
Since it is parallel to X-axis, its slope = 0
∴ `(-(1 + 4"k"))/(1 + 3"k")` = 0
∴ 1 + 4k = 0
∴ k = `-1/4`
Substituting k = `-1/4` in (1), we get
`(x + y - 2) -1/4(4x + 3y - 10)` = 0
∴ 4x + 4y − 8 − 4x − 3y + 10 = 0
∴ y + 2 = 0
This is the equation of required line.
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