[tex]\begin{gathered} \underline{Given-} \\ \end{gathered}[/tex]
[tex]\textsf{4x + 5y = 8}[/tex]
[tex]\textsf{5x + 4y = 12}[/tex]
[tex]\begin{gathered} \underline{★To\: find-} \\ \end{gathered}[/tex]
[tex]\text{the value of x and y in equation?}[/tex]
[tex]\begin{gathered} \underline{★Solution-} \\ \end{gathered}[/tex]
[tex]\sf \leadsto 4x + 5y = 8 - - - (ii)[/tex]
[tex]\sf \leadsto 5x + 4y = 12 - - - (ii)[/tex]
By first equation,
[tex]\sf \leadsto 4x + 5y = 8[/tex]
[tex]\sf \leadsto 4x = 8 - 5y[/tex]
[tex]\sf \leadsto x = \dfrac{8 - 5y}{4}[/tex]
[tex]Now, we can find the original value of Y.[/tex]
[tex]\sf \leadsto 5x + 4y = 12[/tex]
[tex]\sf \leadsto 5 \bigg( \dfrac{8 - 5y}{4} \bigg) + 4y = 12[/tex]
[tex]\sf \leadsto \dfrac{40 - 25y}{4} + 4y = 12[/tex]
[tex]\sf \leadsto \dfrac{40 - 25y + 16y}{4} = 12[/tex]
[tex]\sf \leadsto \dfrac{40 - 9y}{4} = 12[/tex]
[tex]\sf \leadsto 40 - 9y = 12(4)[/tex]
[tex]\sf \leadsto 40 - 9y = 48[/tex]
[tex]\sf \leadsto -9y = 48 - 40[/tex]
[tex]\sf \leadsto -9y = 8[/tex]
[tex]\sf \leadsto y = \dfrac{ -8}{9}[/tex]
[tex]\begin{gathered} \underline{\textsf{Answer-}}\\\end{gathered}[/tex]
[tex]\begin{gathered}\textsf{Now, we can find the original value of Y.}\\\end{gathered}[/tex]
[tex]\sf \leadsto 5x + 4y = 12[/tex]
[tex]\sf \leadsto 5 \bigg( \dfrac{8 - 5y}{4} \bigg) + 4y = 12[/tex]
[tex]\sf \leadsto \dfrac{40 - 25y}{4} + 4y = 12[/tex]
[tex]\sf \leadsto \dfrac{40 - 25y + 16y}{4} = 12[/tex]
[tex]\sf \leadsto \dfrac{40 - 9y}{4} = 12[/tex]
[tex]\sf \leadsto 40 - 9y = 12(4)[/tex]
[tex]\sf \leadsto 40 - 9y = 48[/tex]
[tex]\sf \leadsto -9y = 48 - 40[/tex]
[tex]\sf \leadsto -9y = 8[/tex]
[tex]\sf \leadsto y = \dfrac{ -8}{9}[/tex]
[tex]\begin{gathered}\textsf{Now, we can find the original value of X.}\\\end{gathered}[/tex]
[tex]\sf \leadsto 4x + 5y = 8[/tex]
[tex]\sf \leadsto 4x + 5 \bigg( \dfrac{ -8}{9} \bigg) = [/tex]
[tex]\sf \leadsto 4x - \dfrac{40}{9} = [/tex]
[tex]\sf \leadsto \dfrac{36x - 40}{9} =[/tex]
[tex]\sf \leadsto 36x - 40 = 8(9)[/tex]
[tex]\sf \leadsto 36x - 40 = 72[/tex]
[tex]\sf \leadsto 36x = 72 + 40[/tex]
[tex]\sf \leadsto 36x = 112[/tex]
[tex]\sf \leadsto x = \dfrac{112}{36}[/tex]
[tex]\begin{gathered} \underline{\textsf{Answer-}}\\\end{gathered}[/tex]
Thus, the values of x and y are -8/9 and 112/36 respectively.
