Question

Please solve this for me using substitution

Answer 1

Explanation:

$\bf \underline{★Given-}$

$\textsf{4x + 5y = 8};$

$\textsf{5x + 4y = 12}$

$\bf \underline{★To\: find-}$

$\textsf{the value of x and y in equation?}$

$\bf \underline{★Solution-}$

$\sf \leadsto 4x + 5y = 8 - - - (i)$

$\sf \leadsto 5x + 4y = 12 - - - (ii)$

By first equation,

$\sf \leadsto 4x + 5y = 8$

$\sf \leadsto 4x = 8 - 5y$

$\sf \leadsto x = \dfrac{8 - 5y}{4}$

$\textsf{Now, we can find the original value of Y.}$

$\sf \leadsto 5x + 4y = 12$

$\sf \leadsto 5 \bigg( \dfrac{8 - 5y}{4} \bigg) + 4y = 12$

$\sf \leadsto \dfrac{40 - 25y}{4} + 4y = 12$

$\sf \leadsto \dfrac{40 - 25y + 16y}{4} = 12$

$\sf \leadsto \dfrac{40 - 9y}{4} = 12$

$\sf \leadsto 40 - 9y = 12(4)$

$\sf \leadsto 40 - 9y = 48$

$\sf \leadsto -9y = 48 - 40$

$\sf \leadsto -9y = 8$

$\sf \leadsto y = \dfrac{ -8}{9}$

$\textsf{Now, we can find the original value of X.}$

$\sf \leadsto 4x + 5y = 8$

$\sf \leadsto 4x + 5 \bigg( \dfrac{ -8}{9} \bigg) = 8$

$\sf \leadsto 4x - \dfrac{40}{9} = 8$

$\sf \leadsto \dfrac{36x - 40}{9} = 8$

$\sf \leadsto 36x - 40 = 8(9)$

$\sf \leadsto 36x - 40 = 72$

$\sf \leadsto 36x = 72 + 40$

$\sf \leadsto 36x = 112$

$\sf \leadsto x = \dfrac{112}{36}$

$\underline{\textsf{Answer-}}$

Therefore, the values of x and y are -8/9 and 112/36 respectively.