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7.1 Solving Linear Systems by Graphing
•Systems of Linear Equations•Solving Systems of Equations by Graphing
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To solve a linear system by ________ first graph each equation separately. Next identify the __________ of both lines and circle it. That ordered pair is the _______ to the system. Check your answer by plugging it back into the ______ of equations.
graphingintersection
solutionsystem
Introduction to System of 2 linear equations
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Solving a System Solving a System GraphicallyGraphically
1. Graph each equation on the same coordinate plane. (USE GRAPH PAPER!!!)
2. If the lines intersect: The point (ordered pair) where the lines intersect is the solution.
3. If the lines do not intersect:a. They are the same line – infinitely many solutions
(they have every point in common).b. They are parallel lines – no solution (they share no
common points).
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System of 2 linear equations (in 2 variables x & y)
• 2 equations with 2 variables (x & y) each.
Ax + By = C Dx + Ey = F
• Solution of a System – an ordered pair (x,y) that makes both equations true.
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Example: Check whether the ordered pairs are solutions of the system.
x-3y= -5-2x+3y=10
A. (1,4)1-3(4)= -51-12= -5-11 = -5*doesn’t work in the 1st
equation, no need to check the 2nd.
Not a solution.
B. (-5,0)-5-3(0)= -5-5 = -5
-2(-5)+3(0)=1010=10
Solution
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Example: Solve the system graphically.2x-2y= -82x+2y=4
(-1,3)
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Example: Solve the system graphically.2x+4y=12
x+2y=6• 1st equation:
x-int (6,0)y-int (0,3)
• 2ND equation:x-int (6,0)y-int (0,3)
• What does this mean?The 2 equations are for the same line!
• many solutions
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Example: Solve graphically: x-y=5 2x-2y=9• 1st equation:
x-int (5,0)y-int (0,-5)
• 2nd equation:x-int (9/2,0)y-int (0,-9/2)
• What do you notice about the lines?
They are parallel! Go ahead, check the slopes!
• No solution!
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AssignmentAssignment::
• Complete 6, E, and F on the note taking guide!