Question

Solve the simultaneous equation 3x-2y=10;4x+3y=5

Answer 1

★ Solution :-

$\sf \leadsto 3x - 2y = 10 - - - (i)$

$\sf \leadsto 4x + 3y = 5 - - - (ii)$

By first equation,

$\sf \leadsto 3x - 2y = 10$

$\sf \leadsto 3x = 10 + 2y$

$\sf \leadsto x = \dfrac{10 + 2y}{3}$

Now, we can find the original value of y.

$\sf \leadsto 4x + 3y = 5$

$\sf \leadsto 4 \bigg( \dfrac{10 + 2y}{3} \bigg) + 3y = 5$

$\sf \leadsto \dfrac{40 + 8y}{3} + 3y = 5$

$\sf \leadsto \dfrac{40 + 8y + 9y}{3} = 5$

$\sf \leadsto \dfrac{40 + 17y}{3} = 5$

$\sf \leadsto 40 + 17y = 5(3)$

$\sf \leadsto 40 + 17y = 15$

$\sf \leadsto 17y = 15 - 40$

$\sf \leadsto 17y = - 25$

$\sf \leadsto y = \dfrac{ - 25}{17}$

Now, we can find the original value of x.

$\sf \leadsto 3x - 2y = 10$

$\sf \leadsto 3x - 2 \bigg( \dfrac{ - 25}{17} \bigg) = 10$

$\sf \leadsto 3x + \dfrac{50}{17} = 10$

$\sf \leadsto \dfrac{51x + 50}{17} = 10$

$\sf \leadsto 51x + 50 = 10(17)$

$\sf \leadsto 51x + 50 = 170$

$\sf \leadsto 51x = 170 - 50$

$\sf \leadsto 51x = 120$

$\sf \leadsto x = \dfrac{120}{51}$

Therefore, the values of x and y are 120/51 and -25/17 respectively.