Solve the system of equations.

x = y−4,

2x−5y = 3

Which one-variable linear equation represents the system of equations?
2(y-4)-5y = 3
2x-5(y-4) = 3
2x-5y = y-4
2x-5(x-4) = 3

To solve the system of equations and determine the one-variable linear equation that represents it, let’s start by substituting one equation into the other.

### Given:
1. \( x = y - 4 \)
2. \( 2x - 5y = 3 \)

We want to express this system as a single equation in terms of one variable.

### Solution:

Since \( x = y - 4 \), substitute \( y - 4 \) for \( x \) in the second equation:

\[
2(y - 4) - 5y = 3
\]

This substitution results in the equation:

\[
2(y - 4) - 5y = 3
\]

### Conclusion:
The correct answer is:
**\( 2(y - 4) - 5y = 3 \)**

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Would you like more detailed steps on solving the equation further, or have any questions?

### Additional Questions
1. How can we solve for \( y \) using this single equation?
2. What steps can we take to find the value of \( x \) once \( y \) is known?
3. How do we verify the solution in both original equations?
4. What is the advantage of substitution in solving systems of equations?
5. Are there alternative methods to solve this system (e.g., elimination)?

### Tip
In systems of equations, substitution is often a helpful method if one of the equations is already solved for a single variable.

Learn how to solve the system of equations x = y−4 and 2x−5y = 3 using substitution. This problem helps students understand how to manipulate algebraic expressions and solve for one variable. Suitable for students in Grades 7-9.

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