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- Hugh bought some magazines that cost $3.95 each and some books that cost $8.95 each. He spent a total of $47.65. Let m represent the number of magazines, b represent the number of books.

# Hugh bought some magazines that cost $3.95 each and some books that cost $8.95 each. He spent a total of $47.65. Let m represent the number of magazines, b represent the number of books.

Know the mathematical model for Hugh's purchases: $3.95 for magazines, $8.95 for books, totaling $47.65.

by Maivizhi A

**Updated **Mar 18, 2024

## Hugh bought some magazines that cost $3.95 each and some books that cost $8.95 each. He spent a total of $47.65. Let m represent the number of magazines and b represent the number of books. Which equation models the situation?

**The equation that models the situation is 3.95m + 8.95b = 47.65.**

Let m represent the number of magazines and b represent the number of books.

The cost of m magazines at $3.95 each is 3.95m. The cost of b books at $8.95 each is 8.95b.

Since the total amount spent is $47.65, we can write the equation:

3.95m + 8.95b = 47.65

So, the equation that models the situation is 3.95m + 8.95b = 47.65.

## System of Linear Equations in Algebra

A system of linear equations in algebra, also called a linear system, refers to a collection of two or more **linear equations** that involve the same **variables**.

Here's a breakdown of the key points:

- Linear equation: An equation where the highest power of each variable is 1. It can be written in the general form of
`ax + by = c`

where`a, b,`

and`c`

are constants and`x`

and`y`

are the variables. - Variable: An unknown quantity represented by a letter, like
`x`

,`y`

, or`z`

. - Solution: A set of values for the variables that makes all the equations in the system true simultaneously.

The following are some important aspects of systems of linear equations:

- Number of solutions: Depending on the relationships between the equations, a system can have:
- One unique solution: This occurs when the lines representing the equations intersect at a single point.
- Infinitely many solutions: This happens when the lines representing the equations coincide (completely overlap).
- No solution: This occurs when the lines representing the equations are parallel but not coincident.

- Solving methods: There are various methods for solving systems of linear equations, including:
- Substitution method: Solve one equation for a variable and substitute that expression into the other equation.
- Elimination method: Manipulate the equations to eliminate one variable and then solve for the remaining variable.
- Matrix method: Represent the system as a matrix and perform operations to solve for the variables.

Understanding systems of linear equations forms the foundation of linear algebra, a branch of mathematics with applications in various fields, including physics, engineering, economics, and computer science.

## Hugh bought some magazines that cost $3.95 each and some books that cost $8.95 each. He spent a total of $47.65. Let m represent the number of magazines and b represent the number of books - FAQs

1. What is a system of linear equations?

A system of linear equations is a collection of two or more linear equations that involve the same variables.

2. What is a linear equation?

A linear equation is an equation where the highest power of each variable is 1, often written in the form ax + by = c.

3. How are variables represented in linear equations?

Variables are represented by letters such as x, y, or z.

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