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Sagot :
Given data:
The first equation is 5x-4y+2z=21.
The second equation is -x-5y+6z= -24.
The third equation is -x-4y+5z=-21.
Multiply 5 by second equation and add first and second equation.
[tex]\begin{gathered} 5(-x-5y+6z)+5x-4y+2z=5(-24)+21 \\ -29y+32z=-99\ldots\ldots\ldots\ldots\ldots\text{......}(A) \end{gathered}[/tex]Multiply 5 by third equation and add first and second equation.
[tex]\begin{gathered} 5(-x-4y+5z)+5x-4y+2z=5(-21)+21 \\ -24y+27z=-84 \\ -8y+9z=-28 \\ z=\frac{8y-28}{9} \end{gathered}[/tex]Substitute the above value of z in equation(A).
[tex]\begin{gathered} -29y+32\frac{(8y-28_{})}{9}=-99 \\ -261y+256y--896=-891 \\ -5y=5 \\ y=-1 \end{gathered}[/tex]The value of z is,
[tex]\begin{gathered} z=\frac{8(-1)-28}{9} \\ =-4 \end{gathered}[/tex]The value of x is,
[tex]\begin{gathered} 5x-4(-1)+2(-4)=21 \\ 5x=25 \\ x=5 \end{gathered}[/tex]Thus, the value of x is 5, the value of y is -1, and the value of z is -4.
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