Linear Equations

For what value(s) of $$a$$, do the pair of linear equations $$x + (a^2-3a+3)y = a^2$$ and $$x + y = 1$$ have:
The path of a train A is given by the equation $$x+2y-4=0$$ and the path of another train B is given by the equation $$2x+4y-12=0$$. will train A and train B at any point?
If $$\dfrac {m+n}{m+3n}=\dfrac {2}{3}$$, find: $$\dfrac {60n^{2}}{3m^{2}+mn}$$.
$$4x=x-6$$ Find the value of$$x$$.
Which of the following is not a linear equation in one variable ? why?
$$2x-1=\dfrac{3}{2}$$
$$x+3y=5$$
$$a=0$$