Question

10/x+y+2/x-y=4 15/x+y-5/x-y=-2 solve by elimination

Answer 1

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Answer 2

10/x+y + 2/x-y =4......(i)

15/x+y -5/x-y = -2......(ii)

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

therefore 10a +2b =4..............(iii)

and 15a -5b = - 2..........(iv)

By using elimination method, multiplying (iii) by 5 and (iv) by 2, we get

50a+10b = 20............(v)

30a -10b = -4....(vi)

Adding (v) and (vi) we get

80a = 16 ; ...a= 1/5

Putting the value of a in (iii) i.e. 10a+2b =4 we get

10*1/5+2b = 4

2+2b =4;

2b =2; b=1

As per our assumption, 1/x+y = a

substituting the value of a as 1/5 in our assumption , we get

1/x+y =1/5;...x+y = 5........(vii).

Similarlry for 1/x-y =b; we get 1/x-y = 1......x-y =1.......(viii)

therefore using elimination, we add (vii) and (viii), we get

2x= 6

x =3

Putting the value of x in (vii), we get

3+y=5

y= 2

THE VALUE OF x = 3 AND y = 2