Question 153589
0x + 5y -7z  = 14
2x + y + 4z  = 10
2x + 6y - 3z = 30 
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Switch line 1 and line 2 to get:
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2x + y + 4z  = 10
0x + 5y -7z  = 14
2x + 6y - 3z = 30
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Subtract line 1 from line 3: 
2x + y + 4z  = 10
0x + 5y -7z  = 14
0x + 5y -7z  = 20
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2x + y + 4z  = 10
0x + 5y -7z  = 14
0x + 0y -0z  = 6
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The 3rd line is a contradiction and indicates there is no
solution to the system of three equations.
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Cheers,
Stan H.