Determine the number of solutions for the system without solving.

3x+12y=-27
4x+2y=34

2 answers

Transform each equation to the form
y=mx+b
where m=slope and b=y-intercept.

If the slopes (m) are distinct (different), then there is one solution.

If the slopes are identical, then check the y-intercepts. If the y-intercepts are different, there is no solution (lines are parallel and distinct).

If the slopes are identical and the y-intercepts 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?

3x-9y=0
-x+3y=-3
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