Question

Solve the following system of equations:
$8v-3u=5uv$
$6v-5u=-2uv$

• A.
• B.
• C. Both A and B
• D. None of these

Answer 1

The correct option is B

Divide the given equations by uv,
$8v-3u=5uv\Rightarrow \frac{8}{u}-\frac{3}{v}=5...\left(1\right)$
$6v-5u=-2uv\Rightarrow \frac{6}{u}-\frac{5}{v}=-2...\left(2\right)$
Assume $\frac{1}{u}=x$ and $\frac{1}{v}=y$
Put the values of $\frac{1}{u}$ and $\frac{1}{v}$ in (1) and (2)
$8x-3y=5...\left(3\right)$
$6x-5y=-2...\left(4\right)$
Solving equations (3) and (4) we get x and y
So, $u=\frac{22}{31}$ and $v=\frac{11}{23}$