Question

3 X upon 2 minus 5 upon 3 equals to minus 2 and X upon 3 + 5 upon 2 equals to 13 upon 6​

Answer 1

Given as :

The linear equation as

$\dfrac{3x}{2}$ - $\dfrac{5y}{3}$ = -2

$\dfrac{x}{3}$ + $\dfrac{y}{2}$ = $\dfrac{13}{6}$

To Find : The value of x and y

Solution:

A/Q

$\dfrac{3x}{2}$ - $\dfrac{5y}{3}$ = -2                               .........1

Or, Take LCM of 2 and 3

i.e   $\dfrac{3x \times 3- 5y \times 2}{6}$ = - 2

Or,  9 x - 10 y = - 12                .............a

And

$\dfrac{x}{3}$ + $\dfrac{y}{2}$ = $\dfrac{13}{6}$                                  ........2

Take LCM of 2 and 3

 $\dfrac{x \times 2+ y \times 3}{6}$ = $\dfrac{13}{6}$    

Or, 2 x + 3 y = 13                 ............b

Solving eq a and b , we get

3 × ( 9 x - 10 y ) + 10 × ( 2 x + 3 y ) = 3 × (-12) + 10 × 13

or, 27 x - 30 y + 20 x + 30 y = - 36 + 130

Or, 47 x + 0 = 94

Or, 47 x = 97

∴         x = $\dfrac{94}{47}$

i.e      x = 2

Now, Put the value of x into eq b , we get

2 x + 3 y = 13

or, 2 × 2 + 3 y = 13

Or,            3 y  = 13 - 4

Or,            3 y = 9

∴                  y = $\dfrac{9}{3}$

i.e                 y = 3

Hence, The value of x is 2 and The value of y is 3 . Answer