Let's solve this system of linear equations step by step using the elimination method.
Given the system of equations:
1. 3u + 3v = 15,
2. -2u + 3v = -5.
With the elimination method, we're going to add or subtract the equations in a way that allows us to eliminate one of the variables. Looking at these two equations, it happens that if we add them, the 'v' variable will be eliminated. Let's do this.
Adding eq#1 & eq#2:
(3u + 3v) + (-2u + 3v) = 15 + -5.
That simplifies to u = 10.
Now that we've solved for u, we can substitute this into the other equation to solve for the other variable. Substituting u = 10 into the first equation gives us:
3*10 + 3v = 15,
30 + 3v = 15,
3v = 15 - 30,
3v = -15,
v = -15/3,
v = -5.
Therefore, the solution to the system of equations is u = 10, v = -5.