Question

Solve the following systems of equations:

`15/u + 2/v = 17`

Answer 1

Let 1/u = x and 1/v = y then, the given system of equations become

`15x + 2y = 17 ....(ii)`

`x + y = 36/5` ....(ii)

From (i), we get

2y = 17 - 15x

`=> y = (17 - 15x )/2`

Substituting y = `(17 - 15x)/2` in equation (ii), we get

`x + (17 - 15x)/2 = 36/15`

`=> (2x + 17 - 15x)/2  = 36/5`

`=> (-13x + 17)/2= 36/5`

`=> 5(-13x + 17) = 36xx 2`

=> -65x + 85 = 72

=> -65 = -13

`=> 65x = (=13)/(-65) = 1/5`

Putting x = 1/5 in equation (ii), we get

`1/5 + y = 36/5`

`=> y = 36/5 - 1/5`

So, the solution off the given system of equation is u = 5, v = 1/7