Math Problem Statement

Anthony is solving a system of linear equations using substitution: 6x - 2y = 10 and y = 3x - 5. Which equation represents the first step for Anthony to solve the system?

Solution

To solve the system using substitution, Anthony should replace yy in the first equation with the expression given for yy in the second equation. Here's the process:

The system is: 6x2y=106x - 2y = 10 y=3x5y = 3x - 5

Substituting y=3x5y = 3x - 5 into the first equation: 6x2(3x5)=106x - 2(3x - 5) = 10

This matches option B: 6x2(3x5)=106x - 2(3x - 5) = 10.

So, the correct answer is B.

Would you like further explanation on how this substitution works?

Related Questions

  1. How do you solve the system of equations after substitution?
  2. What happens if you solve the equations using the elimination method instead of substitution?
  3. Can substitution be used for all types of systems of linear equations?
  4. What is the next step after substituting the expression for yy into the equation?
  5. Why is substitution an effective method for solving systems of equations?

Tip: Always isolate one variable first if possible when using the substitution method to simplify the process!

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations
Substitution Method

Formulas

Substitution in a system of equations

Theorems

Substitution method in solving systems of linear equations

Suitable Grade Level

Grades 7-9