Math Problem Statement

Solve each system of equations: 2x + 3y = 6, x = 3

Solution

Let's solve the given system of equations:

  1. 2x+3y=62x + 3y = 6
  2. x=3x = 3

Since the value of xx is already given as 33, we can substitute x=3x = 3 into the first equation.

Substitute into 2x+3y=62x + 3y = 6:

2(3)+3y=62(3) + 3y = 6

This simplifies to:

6+3y=66 + 3y = 6

Now, subtract 6 from both sides:

3y=03y = 0

Finally, divide both sides by 3:

y=0y = 0

Thus, the solution to the system is:

x=3andy=0x = 3 \quad \text{and} \quad y = 0

If you have any further questions or would like more details on the solution process, feel free to ask!


Here are some related questions you may find useful:

  1. What are the different methods to solve a system of linear equations (e.g., substitution, elimination)?
  2. How do you solve systems of equations with two variables using matrices?
  3. How can you graphically represent the solution to a system of linear equations?
  4. What is the significance of parallel lines in a system of equations?
  5. How do you solve systems of equations with three variables?

Tip: When substituting into equations, always double-check the values to avoid calculation errors!

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Math Problem Analysis

Mathematical Concepts

Algebra
Systems of Equations
Substitution Method

Formulas

2x + 3y = 6
x = 3

Theorems

Substitution method to solve systems of equations

Suitable Grade Level

Grades 7-9