How many solutions does the system have?

A

Step-by-step explanation:

There are 2 ways to solve this problem.

Solution 1:

Since we are given two equations, we set them equal to each other to find where they intersect, the solution.

3x+3=-2x+3                              [combine like terms]

5x=0                                         [divide both sides by 5]

x=0

Now that we have x=0, we can plug it into either equation to find the point of intersection.

y=3(0)+3

y=3

We know that the point of intersection is (0,3).

Solution 2:

This way of solving the problem doesn't require any calculations. All it requires is an understanding of slope-intercept form equation. From the two equations given, we know that they are linear lines. Linear lines can only intersect once. Knowing this, we know that there can only be exactly one solution.