Question

Solve:
2(3u - v) = 5uv
2(u + 3v) = 5uv

• A. u = 2, v = 1
• B. u = 3, v = 2
• C. u = 4, v = 3
• D. Insufficient data
• E. None of the above

Answer 1

The correct option is A u = 2, v = 1

$2(3u-v)=5uv\Rightarrow \frac{6}{v}-\frac{2}{u}=5$

$2(u+3v)=5uv\Rightarrow \frac{2}{v}+\frac{6}{u}=5$

Putting $\frac{1}{v}=x$ and $\frac{1}{u}=y$, we get

$6x-2y=5\dots \dots \left(1\right)$

$2x+6y=-2\dots \dots \left(2\right)$

Multiplying Equation (1), and Equation (2) by 3 and 1 respectively, we have

$18x-6y=15$ and $2x+6y=5$

Adding these two equations, we get $20x=20$, i.e., $x=1$

From Equation (1), $y=\left(\frac{6x-5}{2}\right)=\left(\frac{6\times 1-5}{2}\right)=\frac{1}{2}$

$\therefore u=\frac{1}{y}=2$ and $v=\frac{1}{x}=1$