Solving Systems of Linear Equations by Substitution

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Presentation transcript:

Solving Systems of Linear Equations by Substitution October 20 Ms. Stack

10/20 Do Now Is (3, 2) a solution of the system of equations? 2x + y = 8 -x + 3y = 4 How does the graph look when there is “no solution”? How does the graph look when there are “infinitely many solutions”? Solve: 2x + 5y= 10 3x + 7y= 12

What is Substitution? Substitution is when you replace one thing with another thing. Substitution is ideal to use if one of the variables has already been isolated in the original system of equations. Example: y = -2x + 3

Example 1 Solve the following system of linear equations using substitution. x + y = 56 y = 7x (1) (2) From (2) substitute y = 7x into equation (1). x + y = 56

Example 2 Solve the system of equations using substitution: x= -2y

Example 3 Solve the system of equations using substitution: 5x + 8y= 14 4x = 24

Example 4 Solve using substitution: x= y + 3 -2x + 3y= 15

Guided Practice Work through the examples at your own pace, let me know if you need help! There is a solution station to check your work 

Class Discussion 1. What are the three ways we learned how to solve systems? Which method would you use to solve the following: 2. Y=3x + 4 and y= -1/2x + 5 3. x= -5y and 2y + 6x= 20 4. -2x + 5y= 6 and 2x – 7y= 15

Exit Ticket Solve: x=y x+ 2y= 3 Solve: y=-x + 4 y=3x Solve: y=3x 2x + 3y= 10