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

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Presentation transcript:

+ Unit 1 – First-Degree Equations and Inequalities Chapter 3 – Systems of Equations and Inequalities 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

+ 3.2 – Solving Systems of Equations Algebraically Substitution method – 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

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

+ 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?

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

+ 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

+ 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

+ 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

+ 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

+ 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

+ 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

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