Question

solve the following simultaneous equation 1)2x-3y=9 ; 2x+y=12​

Answer 1

Answer:

x=45/8 , y=3/4

Step-by-step explanation:

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Answer 2

★ Solution :-

$\sf \leadsto 2x - 3y = 9 \: \: --- (i)$

$\sf \leadsto 2x + y = 12 \: \: --- (ii)$

By first equation,

$\sf \leadsto 2x - 3y = 9$

$\sf \leadsto 2x = 9 + 3y$

$\sf \leadsto x = \dfrac{9 + 3y}{2}$

Now, we will find the original value of y.

$\sf \leadsto 2x + y = 12$

$\sf \leadsto 2 \bigg( \dfrac{9 + 3y}{2} \bigg) + y = 12$

$\sf \leadsto \dfrac{18 + 6y}{2} + y = 12$

$\sf \leadsto \dfrac{18 + 6y + 2y}{2} = 12$

$\sf \leadsto \dfrac{18 + 8y}{2} = 12$

$\sf \leadsto 18 + 8y = 12(2)$

$\sf \leadsto 18 + 8y = 24$

$\sf \leadsto 8y = 24 - 18$

$\sf \leadsto 8y = 6$

$\sf \leadsto y = \dfrac{6}{8}$

$\sf \leadsto y = \dfrac{3}{4}$

Now, we will find the original value of x.

$\sf \leadsto 2x - 3y = 9$

$\sf \leadsto 2x - 3 \bigg( \dfrac{3}{4} \bigg) = 9$

$\sf \leadsto 2x - \dfrac{9}{4} = 9$

$\sf \leadsto \dfrac{8x - 9}{4} = 9$

$\sf \leadsto 8x - 9 = 9(4)$

$\sf \leadsto 8x - 9 = 36$

$\sf \leadsto 8x = 36 + 9$

$\sf \leadsto 8x = 45$

$\sf \leadsto x = \dfrac{45}{8}$

Therefore, the value of x and y are 45/8 and 3/4 respectively.