You can set both equations together
y = -3x + 1
and y = x - 3
we can replace the y of one equation with the other side
-3x+1 = x-3
add 3x on both sides
1 = x + 3x -3
add 3 on both sides
1 + 3 = x+ 3x
simplify
4 = 4x
divide by 4 on both sides
x = 1
y = x - 3
y = 1 - 3
y = 2
So the solution is: (1,2)