Q. 23.7( 70 Votes )

Solve the following simultaneous equations.
i. 2x + y = 5; 3x - y = 5

ii. x - 2y = -1; 2x - y = 7

iii. x + y = 11; 2x - 3y = 7

iv. 2x + y = -2; 3x - y = 7

v. 2x - y = 5; 3x + 2y = 11

vi. x - 2y = -2; x + 2y = 10

Answer :

(i)


2x + y = 5


y = 5 - 2x eq.[1]


3x - y = 5


Using eq.[1] we have


3x - (5 - 2x) = 5


3x - 5 + 2x = 5


5x = 10


x = 2


Using 'x' in eq.[1]


y = 5 - 2(2)


y = 5 - 4 = 1 cm


(ii)


x - 2y = -1


x = 2y - 1 eq.[1]


2x - y = 7


Using eq.[1], we have


2(2y - 1) - y = 7


4y - 2 - y = 7


3y = 9


y = 3


Using this value in eq.[1]


x = 2(3) - 1


x = 5


(iii)


x + y = 11


y = 11 - x eq.[1]


2x - 3y = 7


Using eq.[1], we have


2x - 3(11 - x) = 7


2x - 33 + 3x = 7


5x = 40


x = 8


Using this in eq.[1]


y = 11 - 8


y = 3


(iv)


2x + y = -2


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


3x - y = 7


Using eq.[1]


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


3x + 2x + 2 =7


5x = 5


x = 1


Using this in eq.[1]


y = -2(1) - 2


y = -2 - 2 = -4


(v)


2x - y = 5


y = 2x - 5 eq.[1]


3x + 2y = 11


Using eq.[1]


3x + 2(2x - 5) = 11


3x + 4x - 10 = 11


7x = 21


x = 3


Using this in eq.[1]


y = 2(3) - 5


y = 1


(vi)


x - 2y = -2


x = 2y - 2 eq.[1]


x + 2y = 10


using eq.[1], we have


2y - 2 + 2y = 10


4y = 12


y = 3


Using this in eq.[1]


x = 2(3) - 2


x = 4


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