Question

2x/3+3y/4=7,5x-3y=18 simultanious linear eqution

Answer 1

$\large \green{ \underline{answer}} \\ \\ \large \implies \therefore \orange{ \boxed{ \: \: \: x =6 \: \: \: \: \: and \: \: \: \: y = 4 }} \\ \\ \large \implies \orange{ \underline{step \: - \: by \: - \: step \: \: \: explanation}} \\ \\ \large \implies{1) = \frac{2x}{3} + \frac{3y}{4} = 7......... (1) } \\ \\ \large \implies{2) = 5x - 3y = 18........(2)} \\ \\ \large \implies{we \: \: can \: \: write \: \: as \: \: equation \:( 1)} \\ \\ \large \implies{8x + 9y = 84....(1)} \\ \\ \large \implies{5x - 3y = 18....(2)} \\ \\ \large \implies{multiply \: \: equation \: \: (1) \: \: by \: \: 1 \: \: } \\ \\ \large \implies{multiply \: \: equation \: \: (2) \: by \: \: 3} \\ \\ \large \implies \therefore{equation \: \: \: will \: \: be \: \: \: written \: \: as} \\ \\ \large \implies{8x + 9y = 84...(1)} \\ \\ \large \implies{15x - 9y = 54....(2)} \\ \\ \large \implies{23x = 138} \\ \\ \large \implies{x = 6} \\ \\ \large \implies{put \: \: the \: \: value \: \: of \: \: x \: \: in \: \: equation \: \: (2)} \\ \\ \large \implies{y = 4} \\ \\ \large \implies \therefore \green{ \boxed{ \: \: x = 6 \: \: \: \: and \: \: \: y = 4}}$

Answer 2

$\mathtt{\underline{\underline{Solution}}}$

$\frac{2x}{3} + \frac{3y}{4} = 7 .............(1)\\ \\ 5x - 3y = 18..............(2) \\ \\ we \: can \: also \: write \: it \: as \: eq(1) \\ \\ 8x + 9y = 84.............(3) \\ 5x - 3y = 18..............(4) \\ \\ multiplying \: eq(3) \: by \: 1 \: a nd \: eq(4) \: by \: 3 \\ we \: get \\ = > 1(8x + 9y) = 84 \times 1 \\ = > 8x + 9y = 84..........(5) \\ \\ = > 3(5x - 3y )= 18 \\ = > 15x - 9y = 54............(6) \\ solving \: eq(5) \\ 8x + 9y = 84 \\ = > 2x = 138 \\ = > x = 6 \\ putting \: the \: value \: of \: x \: in \: eq(6) \\ we \: get \\ 15x - 9y = 54 \\ = > 15 \times 6 - 9y = 54 \\ = > y = 4$

$\fbox{x\:=\:6}$

$\fbox{y\:=\:4}$