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System of Linear Equations

System of Linear Equations . Chapter2Section3. Systems of Linear Equations. A system of linear equations consists of two or more linear equations with two variables. The solution to this system is the point of intersection - the shared point ( x,y ) .

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System of Linear Equations

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  1. System of Linear Equations Chapter2Section3

  2. Systems of Linear Equations • A system of linear equations consists of two or more linear equations with two variables. The solution to this system is the point of intersection - the shared point (x,y). • There are several methods for finding this point of intersection: • Graphical • Substitution • Elimination

  3. Graphical Solutions The graphical method for solving systems of equations is the same method use in Section 2.1. The point of intersection of the two equations is the value of x and y that satisfy both equations simultaneously. Example 1 Solve graphically: From the graph you can see the point of intersection (0.5, -5700). This means that when x = 0.5, the y value is -5700. Graphing as a means of solving is not as accurate as the other methods we will discuss.

  4. A Business Model The two equations that make up the system are:

  5. A Business Model Find the point of intersection on your graphing utility. The solution is the point (12, 67,020).

  6. Example 2 First, solve each equation for the function. Then graph.

  7. Substitution

  8. Example 3

  9. Example 4 • Market equilibrium occurs when the supply quantity equals the demand quantity. If the price results in more units supplied than demanded, its called a surplus. If the price results in less units than demanded, its called a shortfall. Answer the following for the system where q is the number of units demanded and p is the price per unit.  demand  supply

  10. Elimination

  11. Example 5

  12. Modeling Systems of Linear Equations

  13. Types of Solutions

  14. Example 8

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