Question 145018
put your equations in slope-intercept form by solving for {{{y}}}, that is, arrange them so that you have them in the form {{{y=mx+b}}}.  Make certain that you have reduced all fractions to the lowest terms.


Once you have done that you will have two equations:


{{{y=m[1]x+b[1]}}} and {{{y=m[2]x+b[2]}}} 



If {{{m[1]<>m[2]}}}, then the lines intersect and there is exactly one element in the solution set for the system.


If {{{m[1]=m[2]}}} and {{{b[1]<>b[2]}}}, then the lines are different but parallel so the solution set to the system is empty.


If {{{m[1]=m[2]}}} and {{{b[1]=b[2]}}}, then the lines are the same line and there are an infinite number of elements in the solution set for the system.