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**Chapter 3 – Linear Systems**

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**Solving Systems Using Tables and Graphs**

Section 3.1

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System of Equations A set of 2 or more equations with the same variables Ex: −3𝑥+2𝑦= 𝑥+2𝑦=−8

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Solution of a System A set of values for variables that makes ALL the equations true. Ex: −3𝑥+2𝑦= 𝑥+2𝑦=−8 Is −4, −2 a solution to the above system?

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**Using a Graph to Find a Solution**

1. Ex: 𝑦=2𝑥−1 𝑦=−2𝑥+5

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You Try 2. Ex: 𝑦= 1 2 𝑥+2 𝑦=−𝑥−1

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Practice 3. Ex: 3𝑥+𝑦=5 𝑥−𝑦=7

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**STEPS Solve each equation for y.**

Carefully graph each equation with a STRAIGHT line. Find the point of intersection (x, y).

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HOMEWORK p. 138 #1, 2, graph and find the solution to each system

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**Warm Up (Day 2) Graph each system to find the solution:**

𝑥−2𝑦= 𝑦−𝑥= 𝑦=2𝑥−3 6𝑥−3𝑦=9

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Three Possibilities…

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**How Can You Tell Without Graphing?**

Solve each equation for y. Compare the slopes. If they are DIFFERENT… the lines will intersect ONE SOLUTION

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**If BOTH slope and intercepts are the same…**

If the slopes are the same, compare the y-intercepts. If those are DIFFERENT… the lines are parallel NO SOLUTION If BOTH slope and intercepts are the same… the lines coincide INFINITELY MANY SOLUTIONS.

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Practice Without graphing, determine whether the system has one solution, no solutions, or infinitely many solutions. 1. −3𝑥+𝑦=4 𝑥− 1 3 𝑦=1

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Practice Without graphing, determine whether the system has one solution, no solutions, or infinitely many solutions. 𝑥+3𝑦=1 4𝑥+𝑦=−3

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Practice Without graphing, determine whether the system has one solution, no solutions, or infinitely many solutions. 3. 𝑦=2𝑥−3 6𝑥−3𝑦=9

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**In the Graphing Calculator**

Put the two equations into Y1 and Y2. They MUST be solved for y! [2nd][CALC][5] for intersect. Hit [ENTER] 3 times, and it will calculate the point (x, y) where they intersect!

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HOMEWORK (day 2) p. 139 #17-23 (w/o graphing, determine whether the system has 0, 1, or infinitely many solutions) #30, 33 (find the solution to the system using the graphing calculator)

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