Question

Solve the following systems of equations:

`x/3 + y/4 =11`

`(5x)/6 - y/3 = -7`

Answer 1

The given equations are:

`x/3 + y/4 =11`...(i)

`(5x)/6 - y/3 = -7` .....(ii)

From (i) we get

`(4x + 3y)/12 = 11`

=> 4x + 3y = 132 ....(iii)

From (ii), we get

`(5x + 2y)/6 = -7`

=> 5x - 2y = -42 ....(iv)

Let us eliminate y from the given equations. The coefficients of y in the equations(iii) and (iv) are 3 and 2 respectively. The L.C.M of 3 and 2 is 6. So, we make the coefficient of y equal to 6 in the two equations.
Multiplying (iii) by 2 and (iv) by 3, we get

8x + 6y = 264 ...(v)

15x - 6x = -126 ...(vi)

Adding (v) and (vi), we get

8x + 15x = 264 - 126

=> 23x = 138

`=> x = 138/23 = 6`

Substituting x = 6 in (iii), we get

4 x 6 + 3y = 132

=> 3y = 132 - 24

3y = 108

`=> y = 108/3 = 36`

Hence, the solution of the given system of equations is x = 6, y = 36.