Determine the number of solutions for the system without solving.

Question

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

Answer 1

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.

Answer 2

How many solutions are there to the following system of equations?

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