Let's break down what Andre and Elena are doing step-by-step for solving this system of equations:

Given system:
$y = 3x \quad \text{(Equation 1)}$
$y = 9x - 30 \quad \text{(Equation 2)}$

Andre’s Approach:

• Andre's first step:
  $3x = 9x - 30$

Here, Andre is substituting $y = 3x$ from Equation 1 into Equation 2. This process eliminates the variable $y$, leaving a single equation in terms of $x$. Now, he just needs to solve for $x$. Rearranging terms, we get:

$3x - 9x = -30 \quad \Rightarrow \quad -6x = -30 \quad \Rightarrow \quad x = 5$

Elena’s Approach:

• Elena's first step:
  She rewrites the system as: $3y = 9x$ $y = 9x - 30$

In this version, it seems like Elena is trying to modify Equation 1 by multiplying both sides by 3, turning it into $3y = 9x$. This might be intended to align the system in a way that makes elimination easier by focusing on multiples of $y$. From here, she could subtract one equation from the other to isolate a variable.

Do you need further steps or clarifications on either of their approaches? Would you like a full solution using either Andre’s or Elena’s method?

5 Questions to Explore Further:

1. What are the benefits of substitution versus elimination when solving systems of equations?
2. How does multiplying equations by constants help in solving a system?
3. What happens if both equations represent the same line?
4. Can systems like these have no solution or infinitely many solutions? How can you tell?
5. How can graphing both equations help verify the solution?

Tip: Always try to simplify the system first and choose the approach (substitution or elimination) that looks easiest for the given problem.