The solution to the given system is (2, 3, 5). This can be determined by solving the system of equations using elimination.
First, add the first equation to the second equation to eliminate the y-term:
5x + z = 7
Next, add the third equation to the first equation to eliminate the x-term:
3y + z = 3
Finally, substitute the expression for z into the expression for x and solve for y:
y = 3
Now that we have the values for x and y, substitute them into one of the original equations to solve for z:
2(2) - 3(3) + z = 0
z = 5
The solution is (2, 3, 5).