Math  number of solution
posted by Shaila on .
Determine the number of solutions for the system without solving.
3x+12y=27
4x+2y=34

Transform each equation to the form
y=mx+b
where m=slope and b=yintercept.
If the slopes (m) are distinct (different), then there is one solution.
If the slopes are identical, then check the yintercepts. If the yintercepts are different, there is no solution (lines are parallel and distinct).
If the slopes are identical and the yintercepts are the same, then there are infinite solutions (lines are coincident).
In this case, there is one solution. 
How many solutions are there to the following system of equations?
3x9y=0
x+3y=3