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Solving by Elimination with 3x3's

STEP 1:  Use:1and2to ditch the x:


1 ) ( x + 2y - 5z = -11 ) ( -4 ) and 2 ) 4x - 3y + 2z = 11

( -4x - 8y + 20z = 44 ) + ( 4x - 3y + 2z = 11 ) = ( -11y + 22z = 55 )
 

STEP 2:  Use:1and3to ditch the x:


1 ) ( x + 2y - 5z = -11 ) ( 3 ) and 3 ) -3x + 5y + 3z = 8

( 3x + 6y - 15z = -33 ) + ( -3x + 5y + 3z = 8 ) = ( 11y - 12z = -25 ) ... put a box around it
 

STEP 3:  Do the 2 x 2...  ditch the y:


( -11y + 22z = 55 ) + ( 11y - 12z = -25 ) = ( 10z = 30 ) ... z = 3 ... circle him and plug him back into -11y + 22z = 55 for z-11y + 22 ( 3 ) = 55 ... -11y + 66 = 55 ... -11y = -11 ... y = 1 ... circle him
 

STEP 4:  Put z = 3 and y = 1 into one of the ORIGINAL equations:


1) x + 2y - 5z = -11 ... x + 2 ( 1 ) - 5 ( 3 ) = -11 ... x + 2 - 15 = -11 ... x - 13 = -11 ... x = 2 ... circle him

So, the answer is  ( 2 , 1 , 3 ).