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**Vocabulary: Chapter Section 5.2.3 Topic: Simultaneous Linear Equations**

An equation has an equal sign. A linear equation can be drawn on an xy graph. It is a straight line. Simultaneous Linear Equations can be solved to find the point where two lines cross on an xy graph.

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Example One. Instructions: Solve the system of equations by using substitution. -10 -10 ÷5 ÷5

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Example Two. Instructions: Solve the system of equations by using substitution. +15 +15 ÷10 ÷10

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Example Three. Instructions: Solve the system of equations by using substitution. -6 -6 -x -x

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Classwork One Instructions: Solve the system of equations by using substitution.

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**2x 2x = 8 x = 4 3x + 4y = 20 x + 4y = 12 x + 4y = 12 3x + 4y = 20**

Example One Instructions: Use elimination. Find the (x,y) coordinates where the lines cross. 3x + 4y = 20 x + 4y = 12 x + 4y = 12 3x + 4y = 20 (4) + 4y = 12 -( x + 4y = 12 ) 2x 8 -4 -4 2x = 8 4y = 8 ÷2 ÷2 ÷4 ÷4 x = 4 (4,2) y = 2

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**x x = 4 2x + 3y = 5 x + 3y = 1 x + 3y = 1 2x + 3y = 5 (4) + 3y = 1**

Example Two Instructions: Use elimination. Find the (x,y) coordinates where the lines cross. 2x + 3y = 5 x + 3y = 1 x + 3y = 1 2x + 3y = 5 (4) + 3y = 1 -( x + 3y = 1 ) x 4 -4 -4 x = 4 3y = -3 ÷3 ÷3 (4,-1) y = -1

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**8x 8x = 16 x = 2 5x - 6y = -32 3x + 6y = 48 3x + 6y = 48 5x - 6y = -32**

Example Three Instructions: Use elimination. Find the (x,y) coordinates where the lines cross. 5x - 6y = x + 6y = 48 3x + 6y = 48 5x - 6y = -32 +( 3x + 6y = 48 ) 3(2) + 6y = 48 6+ 6y = 48 8x 16 8x = 16 -6 -6 6y = 42 x = 2 (2,7) ÷ ÷6 y = 7

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Classwork One Instructions: Solve the system of equations by using elimination.

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Classwork One Instructions: Solve the system of equations by using substitution.

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**3( ) 5y 5y = 10 y = 2 x + 3y = 5 3x + 4y = 5 3x + 9y = 15 3x + 4y = 5**

Example One. Instructions: Use elimination. Find the (x,y) coordinates where the lines cross. x + 3y = 5 3x + 4y = 5 3( ) 3x + 9y = x + 4y = 5 3x + 4y = 5 3x + 9y = 15 -( 3x + 4y = 5 ) 3x + 4(2) = 5 3x + 8 = 5 5y 10 5y = 10 -8 -8 3x = -3 y = 2 (2, -1) x = -1

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**2( ) 3( ) -5x -5x = -5 x = 1 2x + 3y = 5 3x + 2y = 5**

Example Two Instructions: Use elimination. Find the (x,y) coordinates where the lines cross. 2x + 3y = 5 3x + 2y = 5 2( ) 3( ) 4x + 6y = x + 6y = 15 9x + 6y = 15 4x + 6y = 10 -( 9x + 6y = 15 ) 9(1) + 6y = 15 9 + 6y = 15 -5x -5 -5x = -5 -9 -9 6y = 6 x = 1 (1,1) y = 1

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