The teacher wants us to do the following problem by using substitution. I don't think I am doing it right.

4x - 12y =5
-x + 3y = -1

Those two equations are for parallel lines that never intersect. There is no solution.

If you substitute 3y +1 for x in the first equation, you will be led to an equation that cannot be valid, stating that two different constants are equal.

To solve this system of equations by substitution, you need to solve one equation for one variable and substitute it into the other equation. Let's start by solving the second equation for x.

4x - 12y = 5 ---(Equation 1)
-x + 3y = -1 ---(Equation 2)

Step 1: Solve Equation 2 for x.
-x = -1 - 3y
x = 1 + 3y

Now, substitute this expression for x into Equation 1 and solve for y.

Step 2: Substitute x = 1 + 3y into Equation 1.
4(1 + 3y) - 12y = 5
4 + 12y - 12y = 5
4 = 5

As you can see, we end up with the equation 4 = 5, which is not a true statement. This means that there is no valid solution to this system of equations, and the lines represented by these equations are parallel and never intersect.

So, your initial assumption that there is no solution is correct. It is not a mistake you made, but rather a property of the given equations, indicating that there is no common solution to them.