https://file.aiquickdraw.com/mathbot/file/1728615249021twvbhuga.jpg

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.

Solve the system using substitution. Check your answer: 7x - 4y = 1 and 4y = x - 1

Learn how to solve the system of equations 7x - 4y = 1 and 4y = x - 1 using the substitution method. This detailed step-by-step solution explains key algebraic concepts and is suitable for students in Grades 8-10.

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