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## October 7 th , 2011

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**October 7th , 2011**Happy summer Birthday to: Alek Sogan**Solving Linear Systems by Substitution**• What does “substitution” mean? Use it in a sentence.**Solve by Substitution**2x + y = 1 STEPS x + 2y = 5 1) pick 1 of the equations and get a variable by itself x = 5 – 2y - 2y -2y 2) Put a box around the longer side. • copy down the • unused equation**Solve by Substitution**x = 5 – 2y • copy down the • unused equation 2x + y = 1 4) put a small box around the other variable 2(5 – 2y) + y = 1 • replace the small box • with the stuff from the big • box using parenthesis. y = 3 6) Now solve this equation 7) Use this value to find x. (-1,3)**Solving Linear Systems by Substitution**• Solve the linear system by substitution. Check your solution. 1)x = 2y – 6 4x + 6y = 4**Solving Linear Systems by Substitution**• Solve the linear system by substitution. Check your solution. 2) y = 3x + 2 x + 2y = 11**Solving Linear Systems by Substitution**• Solve the linear system by substitution. Check your solution. 3)3x + y = -7 -2x + 4y = 0**Solving Linear Systems by Substitution**• Solve the linear system by substitution. Check your solution. 4)x – y = 3 x + 2y = -6**Solving Linear Systems by Substitution**5)The length of a rectangle is 7cm more than four times the width. If the perimeter of the rectangle is 44cm, what are its dimensions? a. Write an system of linear equations. b. Solve the system by substitution.**Solving Linear Systems by Substitution**6)The sum of the ages of Susan and her mother is 53. Her mother is 11 years more than twice as old as Susan. How old is Susan, and how old is her mother? a. Write an system of linear equations. b. Solve the system by substitution.**Homework**WS do #1 – 5 only Show work!