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3 Variable Linear Systems of Equations

Total questions: 11

Worksheet time: 55mins

Name
Class
Date
1.

Solve the system of equations: 
 x+5y3z=22x+5y-3z=22  
 3x4y+2z=133x-4y+2z=-13  
 2x+3y+4z=32x+3y+4z=3 

a)

 x=1, y=3, z=2x=1,\ y=3,\ z=-2  

b)

 x=1, y=3, z=2x=-1,\ y=-3,\ z=2  

c)

 x=1, y=3, z=2x=1,\ y=-3,\ z=2  

d)

  x=1, y=3, z=2x=1,\ y=3,\ z=2  

2.

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

3.

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

4.

Solve the system of equations: 
 2x3y=3z72x-3y=3z-7  
 4z2x+3y=124z-2x+3y=12  
 4y+2z3x=04y+2z-3x=0 
Note: don't forget to make sure the equations are written in standard form.

a)

 x=2, y=4, z=5x=2,\ y=4,\ z=5  

b)

 x=2, y=4, z=5x=-2,\ y=-4,\ z=5  

c)

 x=2, y=4, z=4x=-2,\ y=4,\ z=-4  

d)

  x=2, y=4, z=5x=-2,\ y=-4,\ z=-5  

5.

Solve the system of equations: 
 2x+3y5z=612x+3y-5z=61  
 x+2y+4z=5x+2y+4z=-5  
 3x+2y3z=473x+2y-3z=47 

a)

 x=5, y=7, z=6x=5,\ y=7,\ z=-6  

b)

 x=5, y=7, z=6x=-5,\ y=7,\ z=-6  

c)

 x=5, y=7, z=6x=5,\ y=-7,\ z=6  

d)

  x=5, y=7, z=6x=5,\ y=7,\ z=6  

6.

Solve the system of equations: 
 2x+6y+4z=82x+6y+4z=8  
 4x+7y+5z=27-4x+7y+5z=27  
 6x+5y8z=396x+5y-8z=39 

a)

 x=3, y=5, z=4x=3,\ y=-5,\ z=-4  

b)

 x=3, y=5, z=4x=-3,\ y=-5,\ z=4  

c)

 x=3, y=5, z=4x=3,\ y=5,\ z=4  

d)

  x=3, y=5, z=4x=-3,\ y=5,\ z=-4  

7.

Solve the system of equations: 
 4x+3y+3z=24x+3y+3z=2  
 3x+7y=2z783x+7y=2z-78  
 5z+4x+4y=205z+4x+4y=20 

a)

 x=4, y=6, z=12x=-4,\ y=6,\ z=12  

b)

 x=4, y=6, z=12x=-4,\ y=-6,\ z=12  

c)

 x=4, y=6, z=12x=4,\ y=-6,\ z=12  

d)

  x=4, y=6, z=12x=4,\ y=6,\ z=12  

8.

Solve the system of equations: 
 x+y+z=2x+y+z=2  
 2x+2y+2z=42x+2y+2z=4  
 3x3y3z=6-3x-3y-3z=-6 

a)

 x=0, y=0, z=0x=0,\ y=0,\ z=0  

b)

 x=1, y=1, z=2x=1,\ y=1,\ z=2  

c)

No solution

d)

 Infinite solutions

9.

Solve the system of equations: 
 xy2z=4x-y-2z=4  
 4x4yz=24x-4y-z=2  
 x+y+2z=3-x+y+2z=-3 

a)

 x=1, y=1, z=0x=1,\ y=-1,\ z=0  

b)

 x=0, y=0, z=1x=0,\ y=0,\ z=1  

c)

No solution

d)

 Infinite solutions

10.

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

a)

 x=2, y=7, z=4x=2,\ y=-7,\ z=-4  

b)

 x=2, y=7, z=4x=2,\ y=7,\ z=4  

c)

No solution

d)

 Infinite solutions

11.

Andrea sells photographs at art fairs. She prices the photos according to size: small photos cost $10, medium photos cost $15, and large photos cost $40. She usually sells as many small photos as medium and large photos combined. She also sells twice as many medium photos as large. A booth at the art fair costs $300.

If her sales go as usual, she will have to sell (a)   small photos to pay for the booth.