Question

Solve the following systems of equations:

${\displaystyle \frac{15}{u}+\frac{2}{v}=17}$

Answer 1

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

${\displaystyle 15x+2y=17....\left(ii\right)}$

${\displaystyle x+y=\frac{36}{5}}$ ....(ii)

From (i), we get

2y = 17 - 15x

${\displaystyle \Rightarrow y=\frac{17-15x}{2}}$

Substituting y = ${\displaystyle \frac{17-15x}{2}}$ in equation (ii), we get

${\displaystyle x+\frac{17-15x}{2}=\frac{36}{15}}$

${\displaystyle \Rightarrow \frac{2x+17-15x}{2} =\frac{36}{5}}$

${\displaystyle \Rightarrow \frac{-13x+17}{2}=\frac{36}{5}}$

${\displaystyle \Rightarrow 5(-13x+17)=36\times 2}$

=> -65x + 85 = 72

=> -65 = -13

${\displaystyle \Rightarrow 65x=\frac{=13}{-65}=\frac{1}{5}}$

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

${\displaystyle \frac{1}{5}+y=\frac{36}{5}}$

${\displaystyle \Rightarrow y=\frac{36}{5}-\frac{1}{5}}$

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