1. Real-Life Applications Systems of Equation
By Navya Dixit

2. Why is Systems of the Equations Important ?
Systems of equations is an important part of the mathematical world today.
It can be used to solve many real-life problems where multiple constraints are used on the same variables
It is used for a variety of things, explained ahead, from cell phone plans to the profits companies earn from business.

3. Systems of Equation in Business Profits
Profit and loss are the key measures in a business.
A system of equations that includes an equation for income and one for expenses can be used to determine profit and loss.
A business makes profits when its revenue is greater than its expenses.
At the starting, many business have very high expenses to get the company started.

4. Business Profits
A business takes time in the beginning to start making profits
EXAMPlE y= Revenue x= # of products sold
y= 20X (revenue earned from x number of products0
Y= x (each product cost $2 to make and there is in expenses)

5. Business Profits
The company wants to know how many products they have to sell to start collecting profits.
y= 20X
Y= x
After solving, the company has to sell 455 products to start making profits

6. Business Profits
Example of Business profits using systems of equation

7. Solving a Mixture Problem
Companies who make products such as perfume , drinks, chocolate, and more need to know what percentage of one product plus the percentage of another product would equal the final percentage they wanted.
An example would be how many ounces of 70% dark chocolate and 20% milk chocolate you need to mix to get one pound of 40% chocolate?

8. Solving a Mixture Problem
Another example could be making chemicals to get the preferred results. Chemists every day need to find out how much of each chemical to use in a reaction. One way to do this is through systems of equation.
A chemist has a 25% and a 50% acid solution. How much of each solution should be used
to form 200 mL of a 35% acid solution?

9. Solving a Distance-Rate-Time Problem
Sailors need to find out how long it will take to get upstream and downstream based on the currents at different parts of the day so that they can be on schedule. This is also the same concept for planes.
Example: A plane flies 480 mi in an easterly direction, with the wind, in 4 h. Returning westerly along the same route, against the wind, the plane takes 6 h. What is the rate of the plane in still air? What is the rate of the wind?

10. Solving a Distance-Rate-Time Problem
Example of water currents

11. Investment.
When banks or people need to find out how much money they have invested, what the investment rate is, what the total from the annual interest is, they can use systems of equation.
An example would be Donald has investments totaling $8000 in two accounts—one a savings account paying 6% interest, and the other a bond paying 9%. If the annual interest from the two investments was $600, how much did he have invested at each rate?

12. Economics
Systems of equations are used in economics when companies or sellers are trying to find the supply and demand. This is important because they do not want to make many products which can’t be sold and neither do they want to make less.
An example would be Suppose the demand equation for a product is D p and the
supply equation is S 12p. Find the equilibrium point for the product

13. Consumer affairs
Consumers affairs is important for costumers if they want to find out which brand, or company is cheaper for what number of days. This can include cell phone plans, cable, and cars.
An example would be Company A: $30/day and 22¢/mi.
Company B: $28/day and 26¢/mi.
For a 2-day rental, at what number of miles will the charges be the same?

14. Consumer affairs
Example of Consumer affairs using systems of equation