How do you solve the system a + b + 2c = -11, a - 6b +3c = 22, 2a - 4b + c = 14?

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Answer 1 · 2016-05-02T15:56:37

#S={(-2,-5,-2)}#

Use Elimination Method, Matrices, Determinants, or Graphing to solve. I am going to use the Elimination Method.

#a+b+2c=-11#----> Equation 1 (Eq.1)
#a-6b+3c=22#-->Equation 2 (Eq.2)
#2a-4b+c=14#----> Equation 3 (Eq.3)

Multiply Eq.1 by -1 and then add to Eq.2
#[-a-b-2c=11]#
+#[a-6b+3c=22]#
#-7b+c=33#----> Result 1 (R1)

Multiply Eq.2 by -2 and then add to Eq.3
#[-2a+12b-6c=-44]#
+#[2a-4b+c=14]#
#8b-5c=-30#---> Result 2 (R2)

Multiply R1 by 5 and add to R2
#[-35b+5c=165]#
+#8b-5c=-30#
#-27b=135#
#b=-5#

Put -5 in for b in R1
#-7(-5)+c=33#
#35+c=33#
#c=33-35=-2#

Put -5 for b and -2 for c into Equation 1 and solve for a.
#a-5-4=-11#
#a-9=-11#
#a=-11+9#
#a=-2#

#S={(-2,-5,-2)}#