Question

simultaneous solveit please

Answer 1

22/x+y +15/x-y =5 and 55/x+y +40/x-y =13
22*1/x+y +15*1/x-y=5
55*1/x+y + 40*1/x-y =13
Let 1/x+y=a and 1/x-y =b
therefore
22a+15b=5____________(1)
55a+40b=13___________(2)
Multiply equation no(1) by40 and equation (2) by 15
880a+ 600b=200____________(3)
and
825a+600b=195______________(4)
substracting equation (4) from (3)
880a+600b=200
-825a+600b=195
- -
_______________
55a. =5
a=5/55
a=1/11
put a=1/11in equation (2)
55*1/11+40b=13
5+40b=13
40b=13-5
40b=8
b=8/40
b=1/5
Resubstituting a=1/x+y and b= 1 /x-y
1/x+y =1/11
one, one get cancel
x+y=11________________(5)
and
1/x-y=1/5
one ,one get cancel
x+y=5___________________(6)
Adding equation (5) &(6)
x+y=11
+ x-y =5
_______
2x =16
x= 16/2
x=8
put x=8 in equation (5)

x+y=11
8+y=11
y=11-8
y = 3
therefore
(x,y)=(8,3)

Answer 2

22/x+y +15/x-y =5 and 55/x+y +40/x-y =13

22*1/x+y +15*1/x-y=5

55*1/x+y + 40*1/x-y =13

Let 1/x+y=a and 1/x-y =b

therefore

22a+15b=5____________(1)

55a+40b=13___________(2)

Multiply equation no(1) by40 and equation (2) by 15

880a+ 600b=200____________(3)

and

825a+600b=195______________(4)

substracting equation (4) from (3)

880a+600b=200

-825a+600b=195

- -

_______________

55a. =5

a=5/55

a=1/11

put a=1/11in equation (2)

55*1/11+40b=13

5+40b=13

40b=13-5

40b=8

b=8/40

b=1/5

Resubstituting a=1/x+y and b= 1 /x-y

1/x+y =1/11

one, one get cancel

x+y=11________________(5)

and

1/x-y=1/5

one ,one get cancel

x+y=5___________________(6)

Adding equation (5) &(6)

x+y=11

+ x-y =5

_______

2x =16

x= 16/2

x=8

put x=8 in equation (5)

x+y=11

8+y=11

y=11-8

y = 3

therefore

(x,y)=(8,3)

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