The cost of a notebook two more than the thrice the cost of a pen. Write a linear equation in two 
variables to represent this statement.(represent in two variable). Write two solutions of the equation. Mark x=cost of pen and y=cost of notebook

The given statement is "The cost of a notebook is two more than thrice the cost of a pen."

Let's break it down into a linear equation using two variables:
- Let $ x $ be the cost of the pen.
- Let $ y $ be the cost of the notebook.

The relationship between the cost of the notebook and the pen is:
\[
y = 3x + 2
\]
This is the required linear equation.

### Two solutions of the equation:
1. **Solution 1:**
   Let $ x = 2 $ (cost of pen).
   \[
   y = 3(2) + 2 = 6 + 2 = 8
   \]
   So, one solution is $ (x, y) = (2, 8) $.

2. **Solution 2:**
   Let $ x = 0 $ (cost of pen).
   \[
   y = 3(0) + 2 = 0 + 2 = 2
   \]
   So, another solution is $ (x, y) = (0, 2) $.

The equation $ y = 3x + 2 $ describes the relationship between the cost of the pen and the notebook, and the two solutions are $ (2, 8) $ and $ (0, 2) $.

Would you like further explanation on solving or graphing such linear equations?

Here are 5 related questions for further exploration:
1. What would be the cost of the notebook if the pen costs $5?
2. How would the equation change if the notebook cost was 5 more than twice the cost of the pen?
3. Can you graph the equation $ y = 3x + 2 $ on a coordinate plane?
4. How do you find the slope and intercept from the equation $ y = 3x + 2 $?
5. What is the cost of a pen if the notebook costs $20?

**Tip:** To solve for any variable in a linear equation, substitute known values and perform basic operations (like addition, multiplication, etc.).

The cost of a notebook is two more than thrice the cost of a pen. Write a linear equation in two variables to represent this statement. Mark x as the cost of the pen and y as the cost of the notebook. Write two solutions of the equation.

Learn how to write and solve the linear equation y = 3x + 2, where x is the cost of a pen and y is the cost of a notebook. This problem involves key algebraic concepts of linear equations, suitable for students in Grades 6-8. Includes two example solutions.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation