Answer
$x = 4$ and $y = 3$
Work Step by Step
If $u = \frac{1}{x}$ and $v = \frac{1}{y}$, the system can be written as:
$4u - 3v = 0$
$6u + \frac 32 v = 2$
1. Solve for $u$ in the first equation:
$4u - 3v = 0$
Add 3v to both sides.
$4u = 3v$
Divide both sides by 4:
$u = \frac 34 v$
2. Substitute this value into the second equation, and solve for v:
$6(\frac 34 v) + \frac 32 v = 2$
$\frac {18} 4 v + \frac 3 2 v = 2$
$\frac 92v + \frac 32v = 2$
$\frac {12} 2 v = 2$
$6v = 2$
$v = \frac 26 = \frac 13$
3. Find the value of $u$:
$u = \frac 34 v = \frac 34 (\frac 13) = \frac 14$
4. Calculate x and y
$\frac 1x = u $
$\frac 1 x = \frac{1}{4}$
$x = 4$
$\frac 1y = v$
$\frac 1y = \frac 1 3$
$y = 3$
