The problem presents a system of equations: $y = 3x$ $y = 9x - 30$ It describes two different first steps taken by Andre and Elena to solve the system. Andre's first step is to write the equation $3x = 9x - 30$. Elena's first step is to create a new system: $3y = 9x$ $y = 9x - 30$ The question asks whether we agree with either first step and to explain the reasoning.

1. Problem Description

The problem presents a system of equations:

$y = 3x$

$y = 9x - 30$

It describes two different first steps taken by Andre and Elena to solve the system. Andre's first step is to write the equation $3x = 9x - 30$. Elena's first step is to create a new system:

$3y = 9x$

$y = 9x - 30$

The question asks whether we agree with either first step and to explain the reasoning.

2. Solution Steps

Andre's step involves substitution. Since $y = 3x$, he substitutes $3x$ for $y$ in the second equation $y = 9x - 30$, resulting in $3x = 9x - 30$. This is a valid first step.

Elena's step involves multiplying the first equation by 3, resulting in $3y = 9x$. The second equation remains unchanged: $y = 9x - 30$. This is also a valid first step, although perhaps less efficient than Andre's substitution.

Both are correct, but Andre's is a direct substitution, immediately leading to an equation with only $x$.

3. Final Answer

I agree with both Andre's and Elena's first steps. Andre used substitution correctly, and Elena created an equivalent system of equations by multiplying the first equation by

3.