How do you solve 4r + 5s - 3t = 9, 6r - 3s + 1t = 67, 2r + 0s + 1t = 22?

1 Answer
Mar 5, 2016

r=9, s=-3, t=4

Explanation:

This system of variables is equal to
[[4,5,-3],[6,-3,1],[2,0,1]]*[[r],[s],[t]]=[[9],[67],[22]]
We can solve it in this way
Delta=[[4,5,-3],[6,-3,1],[2,0,1]]=-12+10+0-(18+30+0)=-2-48=-50
Delta r=[[9,5,-3],[67,-3,1],[22,0,1]]=-27+110+0-(198+335+0)=83-533=-450
Delta s=[[4,9,-3],[6,67,1],[2,22,1]]=268+18-396-(-402+88+54)=-110+260=150
Delta t=[[4,5,9],[6,-3,67],[2,0,22]]=-264+670+0-(-54+660+0)=406-606=-200

Finally

r=(Delta r)/Delta=(-450)/-50=9
s=(Delta s)/Delta=150/-50=-3
t=(Delta t)/Delta=(-200)/-50=4