Question 250100
You are given the equations of two lines. There are three possibilites.
The two lines intersect at a single point. (single point)
The two lines are parallel and never intersect (no solution) 
The two lines are different equations for the same line (every point on one line is a solution to the second one).

To solve systems of linear equations you can use any one of several methods
1) Plot the lines and solve them graphiclly
2)Use substitution
3)Use elimination

{{{x + 6y = 4}}}
{{{x = 9 - 6y}}} --> {{{x + 6y = 9}}}

Let's use elimination.
{{{x + 6y = 4}}}
{{{x + 6y = 9}}}   Subtract the second equation from the first one
----------------
{{{0 + 0 = -5}}}
{{{0 = -5}}} Can this be true? No. So these two equations are parallel lines

{{{graph(400,400, -10,10,-10,10, (4-x)/6 , (9-x)/6) }}}