First, solve the first equation for y:
y=-3x+1
Next, substitute this value of y into the second equation:
4x+(-3x+1)=3
Solve for x:
4x-3x=3
x=3
Then, plug this value back into the first equation to find y:
y=-3(3)+1
y=10
Therefore, the solution to the system of equations is (x,y) = (3,10).