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

2. 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

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

4. 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 = x + 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

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

6. 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 = 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

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

8. 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

9. 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

10. 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

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