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**Vocabulary: Chapter Section 6.3.1 Topic: Simultaneous Linear Equations**

Simultaneous Linear Equations can be solved to find the point where two lines cross on an xy graph.

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**2x 2x = 4 x = 2 3x + 4y = 16 x + 4y = 12 x + 4y = 12 3x + 4y = 16**

Example One Instructions: Use elimination. Find the (x,y) coordinates where the lines cross. 3x + 4y = 16 x + 4y = 12 x + 4y = 12 3x + 4y = 16 (2) + 4y = 12 -( x + 4y = 12 ) 2x 4 -2 -2 2x = 4 4y = 10 ÷2 ÷2 ÷4 ÷4 x = 2 (2,10/4) y = 10/4

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

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

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

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**Example Three Instructions: Use elimination**

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

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**(3,-2) (-1,8) Classwork Three**

Instructions: Solve the system of equations by using elimination. (3,-2) (-1,8)

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