Solve the systems of linear equations over the indicated Z_{p}. x+y=1 over Z_{3} y+z=0 x+z=1

ankarskogC

ankarskogC

Answered question

2021-03-25

Solve the systems of linear equations over the indicated Zp.
x+y=1 over Z3
y+z=0
x+z=1

Answer & Explanation

lamanocornudaW

lamanocornudaW

Skilled2021-03-27Added 85 answers

Step 1:Given
The system of linear equations:
x+y=1
y+z=0
x+z=1
Step 2:To determine
Solution of the given system of equations over Z3
Step 3:Solution
Consider the given system of equations:
x+y=1...(1)
y+z=0...(2)
x+z=1...(3)
Subtracting equation 3 from equation 2, we get,
y+z-(x+z)=0-1
y+zxz=1
yx=1...(4)
Now, adding equation 1 & 4, we get,
x+y+(y-x)=1+(-1)
2y=0
y=02=0
y=0 & clearly 0Z3.
Plugging value of y=0 in equation 1, we get,
x+0=1
x=1 & clearly 1Z3
Plugging value of y=0 in equation 2, we get,
0+z=0
z=0 & clearly 0Z3
Step 4:Conclusion
Hence, x=1, y=0, z=0 is the solution of given system of equations.
Jeffrey Jordon

Jeffrey Jordon

Expert2021-11-19Added 2605 answers

Answer is given below (on video)

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