Algebra 3 Lesson 1.8 Objective: SSBAT solve a system of equation by graphing. Standards: M11.D.2.1.4

Algebra 3 Warm – Up 1.8 Graph. y = 3x – 6

What does it mean to say the ordered pair (3, 13) is a solution to the equation y = 2x + 7?

Give 1 solution to each equation using its graph. 1. y = -7x – 5

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Review: A graph of an equation shows all the ordered pairs that are Solutions to that equation. The graphs for the equations y = 3x-2 and y= -x – 6 are shown.  What ordered pair is a solution to both equations?

Continued: What does that mean…  (-1, -5) is a solution to y = 3x – 2 and it is a solution to y = -x – 6 because when you put it into each equation it makes that equation true. -5 = 3(-1) – 2 -5 = -3 – 2 -5 = -5 Checks. -5 = -(-1) – 6 -5 = 1 – 6 -5 = -5 Checks.

System of Equations  A set of 2 or more equations that use the same variables.  We use a brace to keep the equations together. Example:  Linear System – All equations are linear equations.

Solution of a System of Equations  An ordered pair(s) that makes ALL of the equations true (It is a solution to all of the equations)

Solving a System of Equations through Graphing 1. Graph both equations on the same axes 2.The point(s) where the graphs intersect is the solution. You want to draw your lines as accurate as possible  use a ruler

Examples: Solve each System of Equations by Graphing. 1.

To Check: Put the solution point into both equations and see if it works.

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Solving a Systems of Equations on Graphing Calculator 1.Go to y= (top left of your calculator) 2.Enter one equation into y 1 3.Enter the other equation into y 2 4.Hit GRAPH (top right of your calculator 5.Hit 2 nd, TRACE (beside the graph key) 6.Choose the INTERSECT option 7.When you get back to the screen with the graphs, hit ENTER 3 times

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7. Which ordered pair(s) are a solution to the system of equations below? (0, -6), (3, 11), (2, 6), (4, 2)

Homework Worksheet 1.8