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Question

Solve the following equations:
x+y+2z=1
2x+y2z=1
x+y2z=1

A
x=0,y=1 and z=0
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B
x=0,y=2 and z=0
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C
x=0,y=1 and z=1
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D
x=1,y=1 and z=0
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Solution

The correct option is A x=0,y=1 and z=0
We have
x+y+2z=1...........(1)
2x+y2z=1...........(2)
x+y2z=1...........(3)

Adding equations (1) and (2), we get

3x+2y=2............(4)

Adding equations (1) and (3), we get

2x+2y=2............(5)

Subtracting equation (5) from (4), we get

x=0

Putting x=0 in equation 5, we get

0+2y=2

y=1

Putting y=1 and x=0 in equation (1), we get

0+1+2z=1

z=0

Thus, we have

x=0,y=1 and z=0

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