Question

Solve the equation by cross multiplication method 5 upon X + Y - 2 upon x minus y equals to minus one and 15 upon X + Y+ 7 upon x minus y = 210

Answer 1

5/(x+y)-2/(x-y)=-1+15/(x+y)+7/(x-y)

{5(x-y)-2(x+y)}=-1+{15(x-y)+7(x+y)

3x-7y=-1+22x-8y

y+1=19x

x=(y+1)/19

Answer 2

Answer:

1. Let,1/(x+y)=u & 1/ (x-y)=v
2. then,
3. 5u-2v+1=0 (I)
4. 15u+7v-10=0 (ii)
5. Using cross multiplication method
6. u. v. 1.
7. -2. 1. 5. -2
8. 7. -10. 15. 7
9. u/13. =. v/65. = 1/65
10. u=1/x+y=1/5
11. x+y=1/u=5
12. x+y=5 (iii)
13. v=1/x-y=1/1
14. x-y=1/v=1/1
15. x-y=1 (iv)
16. Now,
17. Adding (iv) from (iii)
18. x+y=5
19. x-y=1
21. x+x=5+1
22. 2x=6
23. x=6/2
24. x=3
25. Putting x=3 in (iii)
26. x+y=5
27. 3+y=5
28. y=5-3
29. y=2
30. Hence, x=3 and y=2