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

Answer 1

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.