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Solving by Elimination with 3x3's

STEP 2:  Use1and3to ditch the y:


1 ) ( 2x - y + 5z = 4 ) ( 2 ) and 3 ) -3x + 2y - 6z = -7 ... add them together ... ( 4x - 2y + 10z = 8 ) + ( -3x + 2y - 6z = -7 ) = x + 4z = 1 ... put a box around this equation
 

Now, look at the two boxed guys...  Those are our 2 x 2's!  These will give us the values for x and z...
 

STEP 3:  Solve the 2 x 2...  ditch the x:
 

3x + 6z = 3 and -3 ( x + 4z = 1 )( 3x + 6z = 3 ) + ( -3x - 12z = -3 ) = ( -6z = 0 ), which gives z = 0 ...circle him since it's one of our answers!

Now substitute z = 0 into one of the 2 x 2 guys to get x:

x + 4z = 1 ... x + 4 ( 0 ) = 1 ... x = 1 ... circle him