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Unit 1 – First-Degree Equations and Inequalities

Unit 1 – First-Degree Equations and Inequalities. Chapter 3 – Systems of Equations and Inequalities 3.2 – Solving Systems of Equations Algebraically. 3.2 – Solving Systems of Equations Algebraically. In this section we will review: Solving systems of equations by using substitution

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Unit 1 – First-Degree Equations and Inequalities

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  1. Unit 1 – First-Degree Equations and Inequalities Chapter 3 – Systems of Equations and Inequalities 3.2 – Solving Systems of Equations Algebraically

  2. 3.2 – Solving Systems of Equations Algebraically • In this section we will review: • Solving systems of equations by using substitution • Solving systems of equations by using elimination

  3. 3.2 – Solving Systems of Equations Algebraically • Substitutionmethod – One equation is solved for one variable in terms of the other variable. • The expression is then substituted for the variable in the other equation

  4. 3.2 – Solving Systems of Equations Algebraically • Example 1 • Use substitution to solve the system of equations • x + 4y = 26 • x – 5y = -10

  5. 3.2 – Solving Systems of Equations Algebraically • Example 2 • Lancaster Woodworkers Furniture Store builds two types of wooden outdoor chairs. A rocking chair sells for $265 and an Adirondack chair with footstool sells for $320. The books show that last month, the business earned $13,930 for the 48 outdoor chairs sold. How many rocking chairs were sold?

  6. 3.2 – Solving Systems of Equations Algebraically HOMEWORK Page 127 #12 – 17 all, 24 – 25 all

  7. 3.2 – Solving Systems of Equations Algebraically • Elimination method – eliminate one of the variables by adding the equations. • When you add two true equations, the result is a new equation that is also true

  8. 3.2 – Solving Systems of Equations Algebraically • Example 3 • Use the elimination method to solve the system of equations • x + 2y = 10 • -x – y = -6

  9. 3.2 – Solving Systems of Equations Algebraically • Sometimes adding the two equations will not eliminate either variable. • You may use multiplication to write an equivalent equation so that one of the variables has opposite coefficients in both equations. • When you multiply an equation by a nonzero number, the new equation is equivalent to the original equation

  10. 3.2 – Solving Systems of Equations Algebraically • Example 4 • Use the elimination method to solve the system of equations • 2x + 3y = 12 • 5x – 2y = 11

  11. 3.2 – Solving Systems of Equations Algebraically • If you add two equations and the result is an equation that is: • NEVER true • The system in inconsistent • ALWAYS true • The system is consistent and dependent

  12. 3.2 – Solving Systems of Equations Algebraically • Example 5 • Use the elimination method to solve the system of equations • -3x + 5y = 12 • 6x – 10y = -21

  13. 3.2 – Solving Systems of Equations Algebraically HOMEWORK Page 127 #18 – 23 all, 26 – 27 all

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