Vocabulary: Chapter Section Topic: Simultaneous Linear Equations

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Presentation transcript:

Vocabulary: Chapter Section 6.3.1 Topic: Simultaneous Linear Equations The method of elimination subtracts one equation from the other to solve them.

2x 2x = 6 x = 3 5x + 4y = 16 3x + 4y = 10 3x + 4y = 10 5x + 4y = 16 Example One Instructions: Use elimination. Find the (x,y) coordinates where the lines cross. 5x + 4y = 16 3x + 4y = 10 3x + 4y = 10 5x + 4y = 16 3(3) + 4y = 10 -( 3x + 4y = 10 ) 9+ 4y = 10 2x 6 -9 -9 2x = 6 4y = 1 ÷2 ÷2 ÷4 ÷4 x = 3 (3, ⅟₄) y = 1/4

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

2( ) y y = 5 x + 3y = 5 2x + 5y = 5 2x + 6y = 10 2x + 5y = 5 Example Two. Instructions: Use elimination. Find the (x,y) coordinates where the lines cross. x + 3y = 5 2x + 5y = 5 2( ) 2x + 6y = 10 2x + 5y = 5 2x + 5y = 5 2x + 6y = 10 -( 2x + 5y = 5 ) 2x + 5(5) = 5 2x + 25 = 5 y 5 y = 5 -25 -25 2x = -20 ÷2 ÷2 (-10, 5) x = -10

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

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

13x - 6y = 20 7x + 4y = 18 Classwork Three Instructions: Solve the system of equations by using elimination. 13x - 6y = 20 7x + 4y = 18

2x - 5y = 1 3x + 5y = 14 2x + 3y = 4 x - 2y = -5 2x + 3y = 4 Classwork Four Instructions: Solve the system of equations by using elimination. 2x - 5y = 1 3x + 5y = 14 2x + 3y = 4 x - 2y = -5 2x + 3y = 4 x - 2y = -5

2x + y = 5 3x + 4y = 29 3x+4y=1 2x−y=8 x + 2y = 7 x + 8y = 23 Classwork Five Instructions: Solve the system of equations by using elimination. 2x + y = 5 3x + 4y = 29 3x+4y=1 2x−y=8 x + 2y = 7 x + 8y = 23

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 = 15 3x + 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

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