You need to understand what linear equations are first.
Then, the equations have a unique solution if their slopes are different,
because they will therefore intersect at a single point.
To find their slopes, write the equations in the form y=mx+c, as "m" is the slope, the multiplier of x in this form.
These slopes are different if
which gives a unique solution for
To obtain the co-ordinates of the point of intersection of the lines...
from which the values of x and y follow.
There is no solution if the lines are parallel and do not touch.
This is still the equation of the first line
is the first line
is the second line.
For the slopes to be equal,
This will cause the lines to be the same (touching at all points) if a=5,
hence "a" must not be 5.
There is an infinite number of solutions if and
as the equations will be the equations of the same line.
Then for y being any value "t", x will be 1+2y=1+2t