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planes have no common point ) e.g. solve the system x + 24 + 2 4 Equation 3 x + 84 +72 = 20 2 x + 74 +92 = 23 (3 Sol. Eliminate x from equations Q and (3 using Q : O + 2 4 + 2 = (2) - 3x = 2 4 + 47 = 8 3 - 2 x 0 = (3' 34 + 72 = 15 Next, eliminate from (3 ' using x + 24 + = = 4 2 4 + 42 = 8 7 = 3 we found z ! Back substitute from the last equation going up 2" 24+ 42 = 8 = 24+ 12 = 8 = y= -2 1 x + 2 4 + z = 4 = x+ 2(-2)+ 3 = 4 = x=5 Thus, the system has a unique solution ( x , 4 , 2 ) = ( 5 , - 2, 3 )