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Lesson 1.5: Using Systems of Equations

Lesson 1.5: Using Systems of Equations. Advanced Math Topics Mrs. Mongold. How do you solve a system using matrices?. System of Equations: Consists of two or more equation involving the same variables Example: x + y = 10,000 7x + 9y = 85,000. How do you solve a system using matrices?.

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Lesson 1.5: Using Systems of Equations

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  1. Lesson 1.5: Using Systems of Equations Advanced Math Topics Mrs. Mongold

  2. How do you solve a system using matrices? • System of Equations: Consists of two or more equation involving the same variables • Example: x + y = 10,000 7x + 9y = 85,000

  3. How do you solve a system using matrices? • Augmented Matrix: a matrix form of a linear system of equations obtained from the coefficient matrix and constants • Examples Matrix Equation Augmented Matrix

  4. How do you solve a system using matrices? • Reduced Row Echelon Form (rref): each row contains only 0’s until the first nonzero element, which must be a 1 • Each row has the 1 further to the right than the previous row • All entries above and below the 1st 1 in each row must be 0’s • Examples:

  5. How do you solve a system using matrices? • Something to remember System of Equations in two variables ax + by = c dx + ey = f Matrix Equation Solution

  6. Let’s use the calculators • Using our system from the first slide x + y = 10,000 7x + 9y = 85,000

  7. Additional Examples

  8. Homework • Pg 34/ 3-11 odd

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