To solve this system, we can use the substitution method. This involves solving one equation for one variable and then substituting that expression into the other equation to solve for the other variable.
Using the second equation, we can solve for y:
y = x - 7
Next, we can substitute this expression for y in the first equation:
y = 3x - 1
x - 7 = 3x - 1
Now we can solve for x by simplifying the equation:
x - 3x = -1 + 7
-2x = 6
x = -3
Now that we have solved for x, we can substitute this value back into either of the original equations to solve for y. Let's use the second equation:
y = x - 7
y = -3 - 7
y = -10
Therefore, the solution to the system is (-3, -10).