Question

1/2x+1/3y=6
1/3x+1/2y=13/6
Pair of Linear Equations in Two variables
solve​

Answer 1

1/2 x + 1/3 y = 6 ------------------------[ 1 ]

1/3 x + 1/2 y = 13/6 --------------------[ 2 ]

=> Remember that whenever the opposite sides of the both equations are given like 2x +3y and 3x +2y add the terms we get 5x+5y

=> LCM is 6 for these denominators

1/2x + 1/3y = 6

1/3x + 1/2 y = 1/6

--------------------------

3/6x + 3/6y = 37/6

3/6[x+y] = 37/6

x+y = 37*6/6*3

x+y= 37/3

=> Now we should check for x-y by subtracting the same equations

=> LCM is 6 for these denominators

1/2x + 1/3y = 6

[-] 1/3x [-] 1/2y = [-] 1/6

--------------------------

1/6x -1/6y = 35/6

1/6[x-y]= 35/6

x-y= 35*6/6

x-y= 35

=>Now substitute both of them

x+y = 37/6

x-y= 35

-------------------

2x= 247/6

x= 247/3

and y is -142/3