Answer:
Infinite number of solutions.
Explanation:
Lets start by putting the equations in slope-intercept format of y = mx + b. This helps to understand what the equations are telling us. It turns out that they have a hidden surprise.
1) x + y =3
y = -x + 3
2) 5x + 5y = 15
5y = -5x + 15
y = -x + 3 [!]
These equations are identical. They overlap. That means there are an infinite number of solutions, since every point on one matches the same point on the other, for as long as the line decides to stretch.