Question 1099909
.06x+.07y+.08z=16200
x+y+z=250000
0x+y-z=60000

.06,.07,.08,16200
1,1,1,250000
0,1,-1,60000

SM=150000, Meralco=80000, Manila Water=20000
*[invoke cramers_rule_3x3 .06,.07,.08,16200,1,1,1,250000,0,1,-1,60000]

gauss jordan 
same as elimination without the variables
.06x+.07y+.08z=16200
x+y+z=250000
0x+y-z=60000
original 3*4 matrix
0.06,0.07,0.08,16200
1,1,1,250000
0,1,-1,60000

divide row 1 by 0.06
1,1.16666667,1.33333333,270000
1,1,1,250000
0,1,-1,60000

add  -1*row 1 to row 2
1,1.16666667,1.33333333,270000
0,-0.16666667,-0.33333333,-20000
0,1,-1,60000

add  0*row 1 to row 3
1,1.16666667,1.33333333,270000
0,-0.16666667,-0.33333333,-20000
0,1,-1,60000

divide row 2 by -0.16666667
1,1.16666667,1.33333333,270000
0,1,2.0,120000.0
0,1,-1,60000

add  -1*row 2 to row 3
1,1.16666667,1.33333333,270000
0,1,2.0,120000.0
0,0,-3.0,-60000.0

divide row 3 by -3.0
1,1.16666667,1.33333333,270000
0,1,2.0,120000.0
0,0,1,20000.0

add  -2.0*row 3 to row 2
1,1.16666667,1.33333333,270000
0,1,0,80000.0
0,0,1,20000.0

add  -1.33333333*row 3 to row 1
1,1.16666667,0,243333.333
0,1,0,80000.0
0,0,1,20000.0

add  -1.16666667*row 2 to row 1
1,0,0,150000.0
0,1,0,80000.0
0,0,1,20000.0


1 150000.0
2 80000.0
3 20000.0
done
check
.06*150000+.07*80000+.08*20000=16200
9000+5600+1600=16200
16200=16200