 # Thursday Section 3-1: Graphing Systems of Equations Pages 126-132 in textbook.

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Thursday

Section 3-1: Graphing Systems of Equations Pages 126-132 in textbook

Objectives I can solve systems of equations by graphing them. I can identify the 3 types of solutions to a system of equations

System of Equations When you have 2 or more equations to solve at one time, we call this a system of equations. The solution set to the system is where the graphs intersect. When will 2 lines intersect? If they have different slopes. Let’s look at an example.

Given the following system of equations, solve by graphing. x + y = 6 and 3x – 4y =4 One of the easiest ways to graph is to get these into slope intercept form: x + y = 6 becomes y = -x + 6 3x – 4y = 4 -4y = -3x + 4 y = ¾ x -1

1263457891010 4 3 2 7 5 6 8 9 x- axis y- axis 0 1-2-6 -3-4-5 -7-8-9 1010 -4 -3 -2 -7 -5 -6 -8 -9 0 (4,2) y=-x+6 y=3/4x -1

Calculators I want you each to graph these two equations on your calculators y 1 = -x + 6 y 2 = 3/4x –1 Graph 2 nd, Trace, 5(intersect) Enter, Enter, Enter x=4, y= 2 (4, 2) (ALWAYS an Ordered Pair)

How about graphs with equal slopes y = 3x –3 and y =3x +3 The slope is the same in each of these equations: m=3 What is the solution?

y=3x-3 y=3x+3 No Solution

A slightly different example What is two equations have the same slope and same Y-Intercept 12x - 9y = 27 and 8x – 6y = 18 Then both will solve to: y= 4/3x -3

12x-9y=27 8x-6y=18 Infinite solution

Lines intersect at one point: consistent & independent

BIG PICTURE The solution to a system of equations is where the graphs cross! The solution is always Ordered Pair Format! There are 3 types of solutions –One Solution (Ordered Pair) –No Solution –Infinite Solutions

Homework WS 4-1

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