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Simultaneous Equations: 2 & 3 variables

Total questions: 6

Worksheet time: 11mins

Name
Class
Date
1.

Solve the following systems
 x+y+z=2x+y+z=2  
 3x+2y2z=83x+2y-2z=8  
 2x3y4z=02x-3y-4z=0  

a)

 x=2019, y=3219, z=1419x=\frac{20}{19},\ y=\frac{32}{19},\ z=-\frac{14}{19}  

b)

 x=1419, y=3219, z=2019x=-\frac{14}{19},\ y=\frac{32}{19},\ z=\frac{20}{19}  

c)

 x=3219, y=2019, z=1419x=\frac{32}{19},\ y=\frac{20}{19},\ z=-\frac{14}{19}  

2.

Solve the following systems:
 s2t1=0s-2t-1=0  
 12s+t32=0\frac{1}{2}s+t-\frac{3}{2}=0  
hint: rearrange 

a)

 x=2, y=12x=2,\ y=\frac{1}{2}  

b)

 x=12, y=2x=\frac{1}{2},\ y=2  

c)

 s=2, t=12s=2,\ t=\frac{1}{2}  

d)

 s=12, t=2s=\frac{1}{2},\ t=2  

3.


Solve the following system:
 25x15y1=0\frac{2}{5}x-\frac{1}{5}y-1=0  
 5x+2y8=05x+2y-8=0  

a)

 x=2, y=1x=2,\ y=-1  

b)

 x=1, y=2x=-1,\ y=2  

c)

 y=2, z=1y=2,\ z=-1  

4.

Solve the simultaneous equations
 5x3y+2z=135x-3y+2z=13 
 2x+4y3z=92x+4y-3z=-9 
 4x2y+5z=134x-2y+5z=13  

a)

 x=1, y=2, z=1x=1,\ y=-2,\ z=1  

b)

 x=1, y=1, z=2x=1,\ y=1,\ z=-2  

c)

 x=2, y=1, z=1x=-2,\ y=1,\ z=1  

d)

No answer

5.

Can I use calculator to solve these simultaneous equations?
 xy=3x-y=-3  
 x2+xyy2=5x^2+xy-y^2=-5  

a)

Yes

b)

No

c)

I don't know

6.


Solve these simultaneous equations:
 10z+2=2x4y-10z+2=-2x-4y  
 9y+3x21z=09y+3x-21z=0  
 12z+5y+x1=0-12z+5y+x-1=0  

a)

 x=1, y=3, z=2x=1,\ y=3,\ z=-2  

b)

 x=2, y=3, z=1x=-2,\ y=3,\ z=1  

c)

 x=3, y=1, z=2x=3,\ y=1,\ z=-2  

d)

 x=2, y=3x=-2,\ y=3