word problem solve in matrix form

Question

An oil company wants to mix two grades of rocket fuel costing $3 and $4 per gallon,respectively with purified ethanol costing $8 per gallon to obtain 140 gallons of hybrid fuel costing NASA $6 per gallon. If the oil company also wants the amount of lower grade fuel to be twice that of higher-grade rocket fuel,how many gallons of each variety of fueling product should be mixed? USE A 3 - BY- 4 MATRIX TO SOLVE THE PROBLEM

Answer 1

1 1 1 | 140 
3 4 8 | 840 
1 -2 0| 0 

Now if you can use the calculator to solve, you would get the identity matrix on the left. 
By hand, it is a longer process. 

When you get 
| 1 0 0 | 40| 
| 0 1 0 | 20| 
| 0 0 1 | 80| 

X= 40; y= 20; z= 80 

Checking: 40+20+80= 140 
3(40)+ 4(20) + 8(80)= 840 dollars 
And 40= 2(20)