Question

Solve:
8u - 3v = 5uv
6u - 5v = -2uv

• A. $u=\frac{13}{23},v=\frac{22}{33}$
• B. $u=\frac{11}{5},v=\frac{13}{22}$
• C. $u=\frac{11}{23},v=\frac{22}{31}$
• D. Insufficient data
• E. None of the above

Answer 1

The correct option is C $u=\frac{11}{23},v=\frac{22}{31}$

8u - 3v = 5uv,
6u - 5v = -2uv
Dividing both equations by uv, we get
$\frac{8}{v}-\frac{3}{u}=5and\frac{6}{v}-\frac{5}{u}=-2$,
Putting, $\frac{1}{v}=x$ and $\frac{1}{u}=y$, we get
$8x-3y=5\dots \dots \left(1\right)$
and $6x-5y=-2\dots \dots \left(2\right)$
Multiplying Equation (1) and Equation (2) by 6 and 8, respectively, we have,
$48x-18y=30$ and $48x-40y=16$
Subtracting the second equation from the first, we get
$22y=46$, i.e., $y=-\frac{23}{11}$
From Equation (1), $x=\left(\frac{5+3y}{8}\right)=\frac{(5+3\left(\frac{23}{11}\right))}{8}=\frac{31}{22}$
$\therefore u=\frac{1}{y}=\frac{11}{23}$ and $v=\frac{1}{x}=\frac{22}{31}$