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

Answer 1

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.