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Question

Find the value of x,y and z from the given linear equations: x+y+z=0,2x+5y+7z=0,2x5y+3z=0

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Solution

Let,

x+y+z=0....(1)

2x+5y+7z=0....(2)

2x5y+3z=0....(3)

Adding equation (2) and (3), we get,
2x+5y+7z+2x5y+3z=0
4x+10z=0
4x=10z
x=10z4....(4)

Subtracting (3) from (2), we get,
2x+5y+7z2x+5y3z=0
10y+4z=0
10y=4z
y=4z10....(5)

Substituting the values of x and y in equation (1), we get,

10z4+4z10+z=0

(104+410+1)z=0
z=0(104+410+1)
z=0

Substituting the value of z in equations (4) and (5), we get,

x=0,y=0 as multiplying 0 with any non zero quantity gives us zero only.

Hence, x=y=z=0


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