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The history of system of equations dates back to advanced cultures including the Chinese which is said to be as early as 200 BC.

René Descartes is known as the father of Analytic Geometry. He successfully linked geometry and algebra, which were separate in the 17th century. He solved problems in geometry by converting them into problems in algebra. He discovered this to be a simpler process.

FUN FACT: The Cartesian plane is derived from his name!

Carl Friedrich Gauss is known as a contributor to the discovery of solving systems of equations during the 19th century. He founded Gaussian elimination, which is an algorithm used to solve a system of linear equations involving matrices. Over time, the method using Gaussian elimination can be used without the use of matrix notation. This is commonly used in solving systems of equations.

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Suppose you start a business making and selling wooden swings for the yard. It costs you $1500 for tools and lumber to get started, and the materials for each swing cost $200. Your swings sell for $300. Write and solve a system of equations representing the total cost and revenue of your business. Describe what the solution means in terms of the situation.

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Solve the system of linear equations by elimination.

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Solve the system of linear equations by substitution.

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Solve the system of linear equations by graphing.

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Press the play button to hear the correct answer!

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Solve the system of linear equations by elimination.

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Solve the system of linear equations by substitution.

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Solve the system of linear equations by graphing.

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What is a system?
A system of equations is two or more equations. A solution is the point that makes all equations true.

Types of Solutions
O ne solution (Intersecting Lines) - the solution is the point of intersection of the lines
No solution (Parallel Lines)  - lines are parallel and do not intersect
Infinite many solutions (Coinciding Lines) - lines are identical and intersect at every point

Ways to Find the Solution to a System

1. Graphing

2. Substitution

3. Elimination

There is also a fourth way to find a solution to a system and that is using a matrix. This bulletin will focus on the first three ways.

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We use systems of equations in our everyday life without realizing. Most of our problems we solve usually stay in our mind. Some examples when we are using system of equations:

Rate, Distance and Time

Travel Situations

Finding the Best Deal

Cost and Demand

Real World Example:

Suppose you start a business making and selling wooden swings for the yard. It costs you $1500 for tools and lumber to get started, and the materials for each swing cost $200. Your swings sell for $300. Write and solve a system of equations representing the total cost and revenue of your business. Describe what the solution means in terms of the situation.

Scroll to the bottom to find the steps along with the solution!