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Sagot :
The system of equations describes three planes. If they intersect at one point then they have one solution; if they do not intersect, there are no solutions; If they overlap each other, then there are infinitely many solutions.
Let us solve the system.
Let us multiply the first equation by 2 and we get
[tex]2(3x-y+2z=4)=6x-2y+4x=8[/tex]subtracting this from the second equation gives
[tex]0=-16[/tex]which implies no solutions. These two planes never intersect each other and it doesn't matter what the third plane does (because we want ALL THREE to intersect for a solution); therefore, this system does not have any solutions and hence we leave the blanks empty.
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