What would be the first step in the substitution problem for the following linear system?

y= -3 -x 3x+y=3

To solve the linear system using substitution, the first step is to solve one of the equations for one of the variables. 

Given the system:

1. \( y = -3 - x \)
2. \( 3x + y = 3 \)

The first equation, \( y = -3 - x \), is already solved for \( y \). 

**First Step:** Substitute \( y = -3 - x \) into the second equation.

So, replace \( y \) in the second equation:

\[
3x + (-3 - x) = 3
\]

Now, you can solve for \( x \).

Would you like to proceed with the solution, or do you have any questions?

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Here are 8 related questions to expand your understanding:

1. How would you solve for \( x \) after substitution?
2. What is the next step after finding the value of \( x \)?
3. Can substitution be used for nonlinear systems?
4. How do you check if the solution is correct?
5. What if both equations were already solved for \( y \)?
6. How does substitution compare to the elimination method?
7. What happens if the system has no solution?
8. How would you graphically interpret the solution?

**Tip:** Always simplify the equations as much as possible before starting the substitution method. This makes the process easier.

Understand the first step in solving linear equations using the substitution method. Example problem: y = -3 - x, 3x + y = 3. Learn how to substitute one equation into another and solve for variables step-by-step. Suitable for Grades 9-12.

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