The question asks for the correct first step to solve the given system of equations using the substitution method:

System of Equations:

1. $x = y - 5$
2. $3x - 2y = 1$

Explanation:

The substitution method involves replacing one variable with its equivalent expression from the other equation. From Equation 1, $x = y - 5$. This expression for $x$ can be substituted into Equation 2.

Substituting $x = y - 5$ into $3x - 2y = 1$ gives: $3(y - 5) - 2y = 1$

This matches Option A: "Substitute Equation 1 into Equation 2 for $x$, resulting in $3(y - 5) - 2y = 1$."

Correct Answer: A

Would you like a detailed explanation of how to continue solving the system after this step?

5 Related Questions:

1. What is the substitution method, and when is it most useful in solving systems of equations?
2. How can you verify your solution for a system of linear equations after solving it?
3. What are other methods (besides substitution) for solving systems of equations?
4. How do you solve systems of equations graphically, and how does it compare to substitution?
5. Can substitution always be used for nonlinear systems of equations? Why or why not?

Tip:

Always double-check the substitution process by substituting the values back into both original equations to ensure accuracy.