SOLUTION: i dont know what this is realy called but my teacher told use to do this problem & i keep geting lost... can anyone help me? 3a-2b+2c=1 2a+5b=7+5c c+3+4a=3b

Question 95382This question is from textbook Algebra and Trigonometry
: i dont know what this is realy called but my teacher told use to do this problem & i keep geting lost... can anyone help me?
3a-2b+2c=1
2a+5b=7+5c
c+3+4a=3b This question is from textbook Algebra and Trigonometry

Answer by edjones(8007) (Show Source): You can put this solution on YOUR website!
This problem is a long tough grind but we can do it.
Because so there is so much manipulation it is easy to make an error.
The technical term for what we will do is Gaussian Elimination.
Let's line up all the unknowns, one under the other.
X.3a-2b+2c=1
Y.2a+5b-5c=7
Z.4a-3b+c=-3
Multiply -2 times equation Z and add Z to X.
X.3a-2b+2c=1
Z.-8a+6b-2c=6
-------------
X.-5a+4b=7 this is the sum of X and Z and is the new X. Notice c=0 and the equation is simpler
X.-5a+4b=7
Y.2a+5b-5c=7
Z.4a-3b+c=-3
Multiply 5 times Z and add it to Y
Y. 2a+5b-5c=7
Z. 20a-15b+5c=-15
-----------------
=>22a-10b=8 this is the new Y.
X.-5a+4b=7
Y.22a-10b=8
Z.4a-3b+c=-3
Multiply 2.5 times X and add X and Y
X.-12.5a+10b=17.5
Y.22a-10b=8
--------------
=>9.5a=9.5
a=1 Eureka! the rest is easy.
X. -5+4b=7 4b=12 b=3
Z. 4-9+c=-3 c=-3+5=2
Answer a=1, b=3, c=2
Check: (plug into the original equations)
3a-2b+2c=1 3-6+4=1
2a+5b=7+5c 2+15=7+10
c+3+4a=3b 2+3+4=9
EdJones

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