1. Today: C5 Test Grade Reports/Goal Evaluation 7.1 Instruction Practice No trumpets sound when the important decisions of our life are made. Destiny is made known silently. Agnes DeMille Algebra 1

2. Assignment: PSAE Worksheet #5 – Show work on all problems. No trumpets sound when the important decisions of our life are made. Destiny is made known silently. Agnes DeMille Algebra 1

3. Objectives: 1.Solve a system of equations by graphing. 2.Solve systems from the real world. Vocabulary: system of linear equations, solution to a system, point of intersection Solving Linear Systems by Graphing 7.1

4. We have solved equations like: We found many solutions to the equations like: Now we will find 1 solution to 2 equations like: 3(x – 4) = 5 x + 2(x – 3) = 5 – (x + 4) 2x + 4 = 12 x – 4 = 5 3x + 2y = 12 y = 2x - 5 3x + 2y = 12y = 2x - 5 Solving Linear systems by Graphing 7.1

5. Solving Linear systems by Graphing 7.1 Animal wolves cows bees birds crows fish lions turkeys monkeys alligators equations Group pack herd colony flock murder school pride rafters troop congregation system

6. Solving Linear systems by Graphing 7.1 Vocabulary: system of linear equations – a group of 2 or more equations that are linear – use a set mark { to group them. Vocabulary: system of linear equations To get a 1 solution, you need the same number of equations as variables.

7. Example 1 Solve the System by Graphing Solve the equations: by graphing. 12 345 67 8 910 1 2 3 5 6 4 7 8 9 -6 -4-2 -8 -6 -2 -4 -8 standard form – intercept method slope-intercept form – y-intercept & slope

8. Example 1 Solve the System by Graphing Solve the system by graphing. Solve a System by Graphing 1.Graph both equations. 2.Find the intersection. 3.Check the answer. 12 345 67 8 910 1 2 3 5 6 4 7 8 9 -6 -4-2 -8 -6 -2 -4 -8 (3, 4)

9. Solve the system by graphing. Solve a System by Graphing 1.Graph both equations. 2.Find the intersection. 3.Check the answer. 12 345 67 8 910 1 2 3 5 6 4 7 8 9 -6 -4-2 -8 -6 -2 -4 -8 (-3, 1) Example 1 Solve the System by Graphing

10. Solve the system by graphing. Solve a System by Graphing 1.Graph both equations. 2.Find the intersection. 3.Check the answer. 12 345 67 8 910 1 2 3 5 6 4 7 8 9 -6 -4-2 -8 -6 -2 -4 -8 (1, 3) Example 1 Solve the System by Graphing

11. Solve the system by graphing. Solve a System by Graphing 1.Graph both equations. 2.Find the intersection. 3.Check the answer. 12 345 67 8 910 1 2 3 5 6 4 7 8 9 -6 -4-2 -8 -6 -2 -4 -8 (-3, 6) Example 1 Solve the System by Graphing

12. Solve the system by graphing. Solve a System by Graphing 1.Graph both equations. 2.Find the intersection. 3.Check the answer. 12 345 67 8 910 1 2 3 5 6 4 7 8 9 -6 -4-2 -8 -6 -2 -4 -8 (-3, -3) Example 1 Solve the System by Graphing

13. Solve the system by graphing. Solve a System by Graphing 1.Graph both equations. 2.Find the intersection. 3.Check the answer. 12 345 67 8 910 1 2 3 5 6 4 7 8 9 -6 -4-2 -8 -6 -2 -4 -8 no solution Example 1 Solve the System by Graphing

14. Solve the system by graphing. Solve a System by Graphing 1.Graph both equations. 2.Find the intersection. 3.Check the answer. 12 345 67 8 910 1 2 3 5 6 4 7 8 9 -6 -4-2 -8 -6 -2 -4 -8 infinite solutions Example 1 Solve the System by Graphing

15. Example 2 Real Life Linear System You and your sister each have a savings account for college. You have $2000 and plan to deposit an additional $50 per month At the same time, your sister has a balance of $1600 and she plans to deposit $100 per month. Predict when you and your sister will have the same amount? 8 months Using your TI 1.Type the equations into your Calculator 2.Graph 3.Use Calculate function to find the intersection of the system 4.Find the intersection.

16. Example 2 Real Life Linear System An ecologist is studying the population of two types of fish in a lake. Type A is walleye and currently number 5750, but are decreasing at a rate of 250 per year. Type B is bass with a present count of 3500 and increasing at a rate of 500 per year. When will there be equal amounts of both fish? 3 years Using your TI 1.Type the equations into your Calculator 2.Graph 3.Use Calculate function to find the intersection of the system 4.Find the intersection.

17. Assignment: 7.1 p401 #3-10, … 7.1 How do we solve a system by graphing? Solve a System by Graphing 1.Graph both equations. 2.Find the intersection. 3.Check the answer.

18. Assignment: 7.1 p410 #3-10, 17- 19, 21-35 odd, 36 C5 Progress Report Goal Evaluation No trumpets sound when the important decisions of our life are made. Destiny is made known silently. Agnes DeMille Algebra 1