UPSC NDA I 2016 Mathematics Solved Paper

Concept:A line parallel to the $x$‑axis has a constant $y$‑coordinate.Its equation is $y = \text{(that constant)}$.Explanation:Find the intersection point of the two given lines.Line 1: $x + y + 1 = 0$ Line 2: $3x + 2y + 1 = 0$ From Line 1, write $y = -x - 1$ .Substitute into Line 2:$3x + 2(-x-1) + 1 = 0$ $3x - 2x - 2 + 1 = 0$ $x - 1 = 0$   so $x = 1$.Now use $y = -x - 1$ to get $y = -1 - 1 = -2$.Thus the intersection point is $(1, -2)$.A line through this point and parallel to the $x$‑axis must have $y$ equal to the $y$‑coordinate of the point.Hence the equation is $y = -2$.Rewrite in standard form: $y + 2 = 0$.Answer:$y + 2 = 0$   (Option D).