SOLUTION: Perform an operation on the given system that eliminates the indicated variable. Write the new equivalent system. −5x + 5y − 4z = 4 10x − 9y + z =

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Question 1087784: Perform an operation on the given system that eliminates the indicated variable. Write the new equivalent system.
−5x + 5y − 4z = 4
10x − 9y + z = −20
−x + 9y + z = 8
Eliminate the x-term from the second equation.
Answer by ikleyn(52786)   (Show Source): You can put this solution on YOUR website!
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Nothing can be easier. 

Multiply the first equation by 2 and then add the result to the second equation.


After multiplying, you will get 

-10x + 10y - 8z =   8,    (1')
 10x -  9y +  z = -20,    (2')
  -x +  9y +  z =   8.    (3')

Now add (1') and (2') and write the sum as an updated second equation. You will get

-10x + 10y - 8z =   8,    (1'')
  0x +   y - 7z = -12,    (2'')
  -x +  9y +  z =   8.    (3'')

Variable x is just eliminated. You can write your system in the form

-10x + 10y - 8z =   8,    (1'')
         y - 7z = -12,    (2'')
 -x  +  9y +  z =   8.    (3'')

Done and solved.



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