Which equation in the system is the better substitution equation and why?

5*x* − 3*y*

 = 

−9

*x*

 = 

*y* − 9

The equation 5*x* − 3*y* = −9 is better because the slope is more clearly expressed.The equation *x* = *y* − 9 is better because one variable is already expressed in terms of the other.    The equation 5*x* − 3*y* = −9 is better because it expresses a vertical line.The equation *x* = *y* − 9 is better because it expresses a vertical line.

In the system of equations:

1. \( 5x - 3y = -9 \)
2. \( x = y - 9 \)

The better substitution equation is **\( x = y - 9 \)** because one variable, \( x \), is already expressed explicitly in terms of the other variable, \( y \). This makes substitution easier and more straightforward: you can directly substitute \( y - 9 \) for \( x \) in the first equation, simplifying the system without additional rearrangement.

### Explanation:
- **\( 5x - 3y = -9 \)** would require rearrangement to isolate either \( x \) or \( y \), which adds extra steps.
- **\( x = y - 9 \)** is already solved for \( x \), making it easier to substitute into the other equation.

### Clarification on lines:
- \( x = y - 9 \) represents a diagonal line with slope \( 1 \) (not a vertical line).
- \( 5x - 3y = -9 \) is the equation of a line with slope \( \frac{5}{3} \), not a vertical line either.

Would you like further details or clarifications?

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Here are 5 questions to expand on this topic:

1. How do you substitute \( x = y - 9 \) into the first equation?
2. What is the solution to this system of equations?
3. How do you determine if a line is vertical or horizontal from an equation?
4. Can any equation from a system always be used for substitution?
5. How does slope affect the graph of an equation?

**Tip:** Always choose the equation with a single variable isolated for easier substitution.

Which equation in the system is the better substitution equation and why? 5x − 3y = −9 x = y − 9

Explore which equation is the best for substitution in a system of equations involving 5x - 3y = -9 and x = y - 9. Understand how to use the substitution method to solve this algebra problem. Suitable for students in Grades 8-10.

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