Solving Systems of Equations

Transcription

1 Daily Do from last class Graph y = 2x 6 Write the slope in 3 different ways Write the y intercept Homework Please get out your colored zombie graphing worksheet, I will be collecting it. Lesson 9 7 Solving Systems of Equations By Graphing Your Name Mrs. T / / Notes 1

2 Objective: To be able to determine the solution types of a system of equations as well as what the solutions are using graphing. Virtue: If a solution works for you and it works for some one else then it works for both of you and is THE solution to your problem. Skill: Many real world problems can be solved by a system of equations and if you are good at them then you can bust it out to easily find the solution. The more variables that you must solve for the more equations you need to solve them with, and they can be linear, quadratic, cubic, or anything. 2

3 How many solutions does this have? infinitely many How many solutions does this have? infinitely many 3

4 Out of those infinitely many solutions, Is there any solution that works for both? only one System of Equations Two or more linear equations involving the same variables. Solution to the System of Equations Is an ordered pair that satisfies both equations (a point that is on both lines. Slopes: different Intersect at 1 point Consistent and Independent Slopes: same Y intercept at different locations No Intersection Lines are parallel Intersect nowhere Inconsistent Slopes: same Y intercepts the same Intersects Everywhere Lines are the same Consistent and Dependent 4

5 1. y = x 3 y = x 1 2. x = 2 2x + y = x + 2y = 6 y = x 3 4. y = x 3 2x + 2y = 4 5

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7 How to apply systems of equations Step 1: Define the variables, they should be what we are looking to find. Step 2: Look for two totals, these will be the two constants on the other side of the equal sign. Step 3: Write an expression that equals one of the variables Step 4: Totals are usually adding the variables Differences are subtracting the variables. Blake sold snack bars and magazine subscriptions for a school fundraiser. He sold snack bars for $2 each and magazine subscriptions for $25 each. Blake sold 13 items and earned $141. How many snack bars and how many magazine subscriptions did he sell? 7

8 Summary Objective: To be able to determine the solution types of a system of equations as well as what the solutions are using graphing. Virtue: If a solution works for you and it works for some one else then it works for both of you and is THE solution to your problem. Skill: Many real world problems can be solved by a system of equations and if you are good at them then you can bust it out to easily find the solution. The more variables that you must solve for the more equations you need to solve them with, and they can be linear, quadratic, cubic, or anything. Assignment: Workbooks 5 1 Exit Question How many solutions does each system have? 8

9 Homework Answers 9 7: Homework Answers 5 1: 1. one 2. infinately many 3. no solution 4. one 5. one ( 1, 3) 6. one (1,2) 7. no solution 8. Inf. Many 9. one ( 3,0) 10. one (2,1) 11. one (3,0) 12. Inf. Many 13. no solution 9