Solving System of Linear EquationsElimination Method

Warm-up: solve the linear system by

Eliminationy - 2x = -3y - x = -1

(2,1)

Multiplying one equation

-2x - 5y = 2210x + 3y = 22

(5)(5)( )

-10x - 25y = 11010x + 3y = 22 0 - 22y = 132

- 22y = 132-22 -22

y = -6

-2x - 5y = 22-2x - 5y = 22

-2x - 5(-6) = 22

-2x + 30 = 22- 30 - 30

-2x = -8-2 -2

x = 4

(4, -6)

Your turn!4x + 2y = -10-2x + 3y = 33(2)(2)( )

4x + 2y = -10-4x + 6y = 66

0 + 8y = 56

8y = 568 8

y = 7

4x + 2y = -104x + 2y = -104x + 2(7) = -10

4x + 14 = -10- 14 - 14

4x = -244 4

x = -6

(-6, 7)

Your turn… again!

4x + 10y = 702x - 5y = 25

20y = 20

20 = 20

y = 1

4x + 10y = 70

4x + 10(1) = 70

4x + 10 = 70-10 = -10

4x = 204 4

x = 5

Answer: (5,1)

4x + 10y = 70-4x + 10y = -50-2(2x - 5y = 25)

4x + 10y = 70-4x + 10y = -50

Practice!

2x - y = 9 3x + 4y = -14

Answer: ( 2, -5 )

Hint: multiply the first equation by 4

Multiplying two equations

3x + 5y = 105x + 7y = 10

(5)(5)( )

15x + 25y = 50-15x - 21y = -30

0 + 4y = 20

4y = 204 4

y = 5

3x + 5y = 103x + 5y = 103x + 5(5) = 10

3x + 25 = 10- 25 - 25

3x = -153 3

x = -5

(5, -5)

(-3)(-3)( )

Your Turn!2x - 3y = -113x + 2y = 29

(3)(3)( )

6x - 9y = -33-6x -4y = -580 -13y = -91

-13y = -91-13 -13

y = 7

2x - 3y = -112x - 3y = -112x - 3(7) = -11

2x - 21 = -11+ 21 +21

2x = 102 10

x = 5

(7, 5)

(-2)(-2)( )

Summary: On Solving Linear Systems

(Graphing, Substitution, Elimination Methods)Graphing:

Substitution

Elimination

y = ½x + 1

y = -⅔x

y = 2x - 3y = -3x + 2

y = -½x + 1

y = -5x -1

1.) 2.) 3.)

2x + y = 8y = x - 7

y = 3x - 6 -3x + y = -6

y = x + 4y = 3x

1.) 2.) 3.)

x + 2y = 73x - 2y = 1

8x - 9y = 194x + y = -7

4x - 3y = 113x - 5y = -11

1.) 2.) 3.)

Classwork

8x + 11y = 205x - 11y = -59

2x - 3y = 612x + y = -7

2x - 3y = 5 x + 2y = -1

20x + 3y = 20-20x + 5y = 60

1.) 2.)

3.) 4.)