1. Aim #8.1:How do we solve systems of equations with two variables?

2. Systems of Linear Equations and Their Solutions

3. Two linear equations are called a system of linear equations
Two linear equations are called a system of linear equations. A solution to a system of linear equations in two variables is an ordered pair that satisfies both equations in the system.
The solution of a system of linear equations can sometimes be found by graphing both of the equations in the same rectangular coordinate system. For a system with one solution, the coordinates of the point of intersection give the system’s solution.

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6. Eliminating a Variable Using the Substitution Method

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10. Eliminating a Variable Using the Addition Method

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14. Linear Systems Having No Solution or Infinitely Many Solutions

17. Study Tip

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20. Functions of Business: Break-Even Analysis

22. When we graph a Cost equation and a Revenue equation we can see very easily where the Break-even point is. After this point the company will be making a gain and before this point they will be suffering a Loss. The extent of that gain or loss is seen in the graph.

23. Example

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28. Summary: Answer in complete sentences:
List three ways to solve systems of equations.
Choose two from the above list and explain how to solve.
What is one way to check your solution?