Substitute the value of y in the first equation with the second equation.
6x + 3(1-x) = 15
Simplify and solve for x:
6x + 3 - 3x = 15
3x + 3 = 15
3x = 12
x = 4
Now, substitute the value of x in the second equation to solve for y:
y = 1 - x
y = 1 - 4
y = -3
Therefore, the solution to the system of equations is (4, -3).