Answer :

(i)


x + y = 4 eq.[1]


2x - 5y = 1 eq.[2]


We can write eq.[1] as,


x = 4 - y eq.[3]


Substituting eq.[3] in eq.[2],


2(4 - y) - 5y = 1


8 - 2y - 5y = 1


-7y = -7


y = 1


Substituting 'y' in eq.[3]


x = 4 - 1


x = 3


Hence, solution is x = 3 and y = 1.


(ii)


2x + y = 5 eq.[1]


3x - y = 5 eq.[2]


We can write eq.[1] as,


y = 5 - 2x eq.[3]


Substituting eq.[3] in eq.[2],


3x - (5 - 2x) = 5


3x - 5 + 2x = 5


5x = 10


x = 2


Substituting 'x' in eq.[3]


y = 5 - 2(2)


y = 1


Hence, solution is x = 2 and y = 1.


(iii)


3x - 5y = 16 eq.[1]


x - 3y = 8 eq.[2]


We can write eq.[2] as,


x = 8 + 3y eq.[3]


Substituting eq.[3] in eq.[1],


3(8 + 3y) - 5y = 16


24 + 9y - 5y = 16


4y = -8


y = -2


Substituting 'y' in eq.[3]


x = 8 + 3(-2)


x = 8 - 6 = 2


Hence, solution is x = 2 and y = -2


(iv)


2y - x = 0 eq.[1]


10x + 15y = 105 eq.[2]


We can write eq.[1] as,


x = 2y eq.[3]


Substituting eq.[3] in eq.[2],


10(2y) + 15y = 105


20y + 15y = 105


35y = 105


y = 3


Substituting 'y' in eq.[3]


x = 2(3)


x = 6


Hence, solution is x = 6 and y = 3.


(v)


2x + 3y + 4 = 0 eq.[1]


x - 5y = 11 eq.[2]


We can write eq.[2] as,


x = 11 + 5y eq.[3]


Substituting eq.[3] in eq.[1],


2(11 + 5y) + 3y + 4 = 0


22 + 10y + 3y + 4 = 0


13y + 26 = 0


13y = -26


y = -2


Substituting 'y' in eq.[3]


x = 11 + 5(-2)


x = 11 - 10 = 1


Hence, solution is x = 1 and y = -2.


(vi)


2x - 7y = 7 eq.[1]


3x + y = 22 eq.[2]


We can write eq.[2] as,


y = 22 - 3x eq.[3]


Substituting eq.[3] in eq.[1],


2x - 7(22- 3x) = 7


2x - 154 + 21x = 7


23x = 161


x = 7


Substituting 'x' in eq.[3]


y = 22 - 3(7)


y = 22 - 21 = 1


Hence, solution is x = 7 and y = 1.

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