Solving Linear Systems with 3 Variables

Equations

100

What is the 1st step in solving 3 variable systems?

The first step is to label each equation as A,B and C

200

How many variables are in this system?      
x-2y+z=5 and 2x+y=3

3 Variables 

300

What do you do if the variables aren’t opposite and you can’t eliminat?

You multiply one or both equations by a constant to make them opposites

400

50 x 260

13000

500

What’s the coefficient of z in: 5x-2z+y=0

-2

Solving with 2 Variables

100

(1) 2x+3y=16

(2) 5x-4y=-5

x=2, y=4

200

(1) -6x+6y=6    
(2) 6x-3y=12

 x=5,y=6

300

(1) -2x+6y=4

(2) 2x-2y=8

x=7, y=3

400

(1) x-y=11

(2) 2x+y=19

x=10, y=-1

500

(1) -4x+9y=9

(2) 4(x-3y=-6)

x=-9/5 y=-1

Solving with 3 Variables

100

(1) x+y+z=2 

 (2) -x+3y+2z=8 

 (3) 4x+y=4

x=0, y=4, z=-2

200

(1) x-2y+3z=9

(2) -x+3y-z=-6

(3) 2x-5y+5z=17

x=1, y=-1, z=2

300

(1) -x+4y-2z=2 

(2) -2x-4y+6z=-24 

(3) 4x-4y+5z=-8

x=2, y=-1, z=-4

400

(1) x + y - 2z = 5

(2) -x + 2y + z = 2

(3) 2x + 3y - z = 9

x=1, y=2, z=-1

500

(1) 2x + y - z = 9

(2) -x + 6y + 2z = -17

(3) 5x + 7y + z = 4

x=3, 6=-1, z=-4