Anthony is solving a system of linear equation using substitution.
 
6x−2y=106x−2y=10

y=3x−5y=3x−5


Which equation represents the first step for Anthony to solve the system?

A.6x−3x−5=106x−3x−5=10

B.6(3x−5)−2y=106(3x−5)−2y=10

C.6x−2(3x−5)=106x−2(3x−5)=10

D.6x−2x−5=106x−2x−5=10

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To solve this system using substitution, Anthony would substitute the expression for \( y \) from the second equation \( y = 3x - 5 \) into the first equation \( 6x - 2y = 10 \).

This substitution process involves replacing \( y \) in the first equation with \( 3x - 5 \). Here's how it works step by step:

- The original equation is \( 6x - 2y = 10 \).
- Substitute \( y = 3x - 5 \) into the equation:
  \[
  6x - 2(3x - 5) = 10.
  \]

Thus, the correct answer is **C**: \( 6x - 2(3x - 5) = 10 \).

Would you like more details or have any questions?

Here are five related questions:
1. What would be the next step in solving the equation after substitution?
2. How does substitution compare with the elimination method?
3. Can you solve the system after the substitution step?
4. How do you check if the solution to a system of equations is correct?
5. What are the advantages of using substitution over other methods?

**Tip:** When using substitution, always ensure that you isolate one variable before substituting it into the other equation to avoid errors.

Anthony is solving a system of linear equations using substitution. 

6x − 2y = 10 

y = 3x − 5 

Which equation represents the first step for Anthony to solve the system?

A. 6x − 3x − 5 = 10
B. 6(3x − 5) − 2y = 10
C. 6x − 2(3x − 5) = 10
D. 6x − 2x − 5 = 10

Learn how to solve a system of linear equations using the substitution method. This problem involves substituting y = 3x − 5 into the equation 6x − 2y = 10. Follow the step-by-step process to arrive at the correct solution. Suitable for students in Grades 8-10.

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