Math Problem Statement
The sum of two numbers is 14. The larger number is 2 less than three times the smaller number. Write a system of equations to find these numbers. Let x = smaller number and y = larger number.
Solution
The problem states:
- The sum of two numbers is 14.
- The larger number is 2 less than three times the smaller number.
We need to write a system of equations where:
- = smaller number
- = larger number.
Step-by-Step Formulation:
-
The sum of two numbers is 14:
-
The larger number is 2 less than three times the smaller number:
System of Equations:
x + y = 14 \\ y = 3x - 2 \end{cases}$$ ### Correct Option: The first option: $$x + y = 14, \quad y = 3x - 2$$ --- Let me know if you want me to solve this system for the values of $$x$$ and $$y$$, or if you have any additional questions! --- ### Related Questions: 1. Solve the system of equations $$x + y = 14$$ and $$y = 3x - 2$$. 2. How can substitution be used to solve systems of equations like this? 3. What are other methods for solving systems of equations, like elimination? 4. If $$x = 4$$, what is $$y$$ based on $$y = 3x - 2$$? 5. What happens if the conditions change, such as $$y = 3x + 2$$? ### Tip: Always identify the relationships between variables and translate them step by step into algebraic equations.Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Linear Equations
Systems of Equations
Algebra
Formulas
x + y = 14
y = 3x - 2
Theorems
Basic Linear Equation Theorem
Suitable Grade Level
Grades 8-10