3 Variable Linear Systems of Equations

Solve the system of equations: 
 $x+5y-3z=22$  
 $3x-4y+2z=-13$  
 $2x+3y+4z=3$ 

•  $x=1,\ y=3,\ z=-2$  

•  $x=-1,\ y=-3,\ z=2$  

•  $x=1,\ y=-3,\ z=2$  

•   $x=1,\ y=3,\ z=2$  

If you run into a mathematical statement such as 0=0 when solving a system of 3 linear equations, then the system has __________ solutions.

If you run into a mathematical statement such as 0=4 when solving a system of 3 linear equations, then the system has __________ solutions.

Solve the system of equations: 
 $2x-3y=3z-7$  
 $4z-2x+3y=12$  
 $4y+2z-3x=0$ 
Note: don't forget to make sure the equations are written in standard form.

•  $x=2,\ y=4,\ z=5$  

•  $x=-2,\ y=-4,\ z=5$  

•  $x=-2,\ y=4,\ z=-4$  

•   $x=-2,\ y=-4,\ z=-5$  

Solve the system of equations: 
 $2x+3y-5z=61$  
 $x+2y+4z=-5$  
 $3x+2y-3z=47$ 

•  $x=5,\ y=7,\ z=-6$  

•  $x=-5,\ y=7,\ z=-6$  

•  $x=5,\ y=-7,\ z=6$  

•   $x=5,\ y=7,\ z=6$  

Solve the system of equations: 
 $2x+6y+4z=8$  
 $-4x+7y+5z=27$  
 $6x+5y-8z=39$ 

•  $x=3,\ y=-5,\ z=-4$  

•  $x=-3,\ y=-5,\ z=4$  

•  $x=3,\ y=5,\ z=4$  

•   $x=-3,\ y=5,\ z=-4$  

Solve the system of equations: 
 $4x+3y+3z=2$  
 $3x+7y=2z-78$  
 $5z+4x+4y=20$ 

•  $x=-4,\ y=6,\ z=12$  

•  $x=-4,\ y=-6,\ z=12$  

•  $x=4,\ y=-6,\ z=12$  

•   $x=4,\ y=6,\ z=12$  

Solve the system of equations: 
 $x+y+z=2$  
 $2x+2y+2z=4$  
 $-3x-3y-3z=-6$ 

•  $x=0,\ y=0,\ z=0$  

•  $x=1,\ y=1,\ z=2$  

• No solution

•  Infinite solutions

Solve the system of equations: 
 $x-y-2z=4$  
 $4x-4y-z=2$  
 $-x+y+2z=-3$ 

•  $x=1,\ y=-1,\ z=0$  

•  $x=0,\ y=0,\ z=1$  

• No solution

•  Infinite solutions

Solve the system of equations: 
 $f+g+h=13$  
 $f-h=-2$  
 $-2f+g=3$ 

•  $x=2,\ y=-7,\ z=-4$  

•  $x=2,\ y=7,\ z=4$  

• No solution

•  Infinite solutions