P.4 Math questions

1. y+z+w =6 ......(1)
z+2w+x=8 ......(2)
3w+x+y=10 ......(3)
x+y+z=9 ......(4)

(2)-(1):
w+x-y=2 ……(5)

(4)-(2):
y-2w=1
y=1+2w ……(6)

(4)-(1):
x-w=3
x=w+3 ……(7)

Put (6),(7) into (3)
3w+w+3+1+2w=10
6w=6
w=1

Put w=1 into (6)
y=1+2=3

Put w=1 into (7)
x=1+3=4

Put w=1, y=3 into (1)
3+z+1=6
z=2


2. 1/x - 2/y + 3/z =17
2/x + 3/y - 4/z =-10
3/x - 2/y + 5/z =31

Let 1/x =A, 1/y =B and 1/z=C
A-2B+3C=17 ……(1)
2A+3B-4C=-10 ……(2)
3A-2B+5C=31 ……(3)

(3)-(1):
2A+2C=14
A=7-C ……(4)

2(1)-(2):
-7B+10C=44
B=(10C-44)/7 ……(5)

Put (4),(5) into (1)
7-C-(20C-88)/7+3C=17
C=3

Put C=3 into (4)
A=4

Put C=3 into (5)
B=-2

1/x=4 1/y=-2 1/z=3
x=1/4 y=-1/2 z=1/3


3. x+y+z =5 ......(1)
y+z+w =8 ......(2)
z+w+x =-2 ......(3)
w+x+y =4 ......(4)

(1)+(2)+(3)+(4):
3x+3y+3z+3w=15 .......(5)

(5)/3:
x+y+z+w=5 ......(6)

(6)-(2):
x=-3

(6)-(3):
y=7

(6)-(4):
z=1

(6)-(1):
w=0