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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
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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
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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
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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
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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
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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.
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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
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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)
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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
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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
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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
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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
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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
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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
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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.
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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.
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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.
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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
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