Problem

A set of points $P(x,y)$ is defined by the parametric equations

$$x=\frac{t-1}{2t+1}\qquad y=\frac{6}{2t+1}\qquad t\ne -\frac{1}{2}$$

(a) Show that all points $P(x,y)$ lie on a straight line.

(b) Hence or otherwise, find the $x$ coordinate of the point of intersection of this line and the line with equation $y=x+12$