SOLUTION: 4a+5b-6c=2 -3a-2b+7c=-15 -a+4b+2c=-13 I know the answer is (-3, -2 -4) but can't figure out how to get it

Algebra ->  Expressions-with-variables -> SOLUTION: 4a+5b-6c=2 -3a-2b+7c=-15 -a+4b+2c=-13 I know the answer is (-3, -2 -4) but can't figure out how to get it      Log On


   

Question 672662: 4a+5b-6c=2
-3a-2b+7c=-15
-a+4b+2c=-13
I know the answer is (-3, -2 -4) but can't figure out how to get it
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
There are many ways to do this, but here is one of them.

Convert

4a+5b-6c=2
-3a-2b+7c=-15
-a+4b+2c=-13

to matrix form to get 


4	5	-6	2
-3	-2	7	-15
-1	4	2	-13


Then use row reduction 

4	5	-6	2
-3	-2	7	-15
-1	4	2	-13


1	1.25	-1.5	0.5     	0.25*R1
-3	-2	7	-15	
-1	4	2	-13	


1	1.25	-1.5	0.5	
0	1.75	2.5	-13.5   	R2 + (3)*R1
-1	4	2	-13	


1	1.25	-1.5	0.5	
0	1.75	2.5	-13.5	
0	5.25	0.5	-12.5   	R3 + (1)*R1


1	1.25	-1.5	0.5	
0	1	1.4286	-7.7143 	0.571429*R2
0	5.25	0.5	-12.5	


1	0	-3.2857	10.1429 	R1 + (-1.25)*R2
0	1	1.4286	-7.7143	
0	5.25	0.5	-12.5	


1	0	-3.2857	10.1429	
0	1	1.4286	-7.7143	
0	0	-7	28      	R3 + (-5.25)*R2


1	0	-3.2857	10.1429	
0	1	1.4286	-7.7143	
0	0	1	-4      	-0.142857*R3


1	0	0	-3      	R1 + (3.28571)*R3
0	1	1.4286	-7.7143	
0	0	1	-4	


1	0	0	-3	
0	1	0	-2      	R2 + (-1.42857)*R3
0	0	1	-4


The right hand column is -3, -2, -4

These 3 values correspond to a, b, and c respectively.

So the solutions are...

a = -3

b = -2

c = -4

They form the ordered triple (-3, -2, -4)