Question

3x/2 - 5y/3 = -2 this is equation number one and x/3+y/2= 13/6 by substistion method

Answer 1

$\huge\mathcal{Answer \ :-}$

$\mathsf{Given \ equations \ :-}$

$\frac{3x}{2} - \frac{5y}{3} = - 2$
$\mathsf{On \ further \ solving, \ we \ get}$

$\frac{(3x)(3) - (5y)(2)}{6} = - 2 \\ \\ \frac{9x - 10y}{6} = - 2 \\ \\ 9x - 10y = - 12$

$\mathsf{Another \ equation}$

$\frac{x}{3} + \frac{y}{2} = \frac{13}{6}$
$\mathsf{On \ further \ solving, \ we \ get}$

$\frac{(x)(2) + (y)(3)}{6} = \frac{13}{6} \\ \\ \frac{2x + 3y}{6} = \frac{13}{6} \\ \\ 2x + 3y = 13$

$\mathsf{We \ get \ two \ equations}$

$\mathsf\red{9x - 10y \ = \ -12}$ ____(1)

$\mathsf{And}$

$\mathsf\red{2x + 3y \ = \ 13}$ ____(2)

$\mathsf{From \ (2), \ we \ get}$

$x = \frac{13 - 3y}{2 }$

$\mathsf{Put \ this \ in \ (1), \ we \ get}$

$9( \frac{13 - 3y}{2} ) - 10y = - 12 \\ \\ \frac{117 - 27y}{2} - 10y = - 12 \\ \\ \frac{117 - 27y - 20y}{2} = - 12 \\ \\ 117 - 47y = - 24 \\ \\ - 47y = - 24 - 117 \\ \\ - 47y = - 141 \\ \\ y = 3$

$\mathsf{Now,}$

$x = \frac{13 - 3y}{2 }$

$\mathsf{Putting \ y \ = \ 3}$

$x = \frac{13 - 3(3)}{2} \\ \\ x = \frac{13 - 9}{2} \\ \\ x = \frac{4}{2} \\ \\ x = 2$

$\mathsf\red{x \ = \ 2 \ And \ y \ = \ 3.}$

$\huge\mathbb{Hope \ this \ helps.}$

Answer 2

taking lcm of the eqution 1 = (9x-10y)/6=-2

       =9x-10y = -12

       = 9 x - 10 y + 12 = 0

   =   (2 x +3 y )/ 6 = 13/ 6  equation ...2

   = 2x +3y -13 =0

    find value of x from equation 1

         x =( -12+10y)/9

 put value of x in equation 2

2 (-12 + 10 y ) /9 +3y -13 = 0

(-24+20 y ) /9 + 3y - 13 =0

taking l c m of full eq..

-24 +20y + 27y -117= 0

47 y = 141

y = 3

put value of y in eq... 1

9 x -30 + 12 = 0

9 x = 18

x = 2  hope it help you