Identify the number of solutions to the system of equation:

y=⅓ x + 2
-x +3y = 6

1 answer

To find the number of solutions for a system of equations, we need to determine if the lines represented by the equations intersect, are parallel, or coincide.

The first equation can be rewritten as:
x - 3y = -6

Now we have the system of equations:
-x + 3y = 6
x - 3y = -6

Adding both equations together, we get:
0 = 0

This means the two equations represent the same line, so they coincide. Therefore, there are infinite solutions to the system of equations.