To solve this system of equations using substitution, let's follow the steps:

Given:

1. $7x - 4y = 1$
2. $4y = x - 1$

Step 1: Solve the second equation for $y$:

$4y = x - 1 \implies y = \frac{x - 1}{4}$

Step 2: Substitute $y = \frac{x - 1}{4}$ into the first equation:

$7x - 4\left(\frac{x - 1}{4}\right) = 1$

Simplify this: $7x - (x - 1) = 1$ $7x - x + 1 = 1$ $6x + 1 = 1$

Step 3: Solve for $x$:

$6x = 0 \implies x = 0$

Step 4: Find $y$ using $x = 0$:

Substitute $x = 0$ into $y = \frac{x - 1}{4}$: $y = \frac{0 - 1}{4} = -\frac{1}{4}$

Solution:

The solution to the system is $(0, -\frac{1}{4})$.

Would you like a detailed verification or further explanation on any part?

Here are 5 related questions you might find useful:

1. How do you solve a system of equations using the elimination method?
2. What are other methods for solving systems of equations besides substitution?
3. How can we graphically interpret the solution $(0, -\frac{1}{4})$?
4. What types of solutions can systems of linear equations have (one solution, no solution, infinitely many)?
5. How do you determine if a system of equations is consistent or inconsistent?

Tip: Substitution works best when one of the equations is already solved for a variable, or can be easily manipulated into that form.