Question

4/x + 3y = 14; 3/x - 4y =23

Answer 1

first equation(must get x alone)
$\frac{4}{x} + 3y = 14$
$\frac{4}{x} = 14 - 3y$
$\frac{4}{14 - 3y} = x$
$x = \frac{4}{14 - 3y}$
2nd equation(must get x alone as well)
$\frac{3}{x} - 4y = 23$
$\frac{3}{x} = 23 + 4y$
$\frac{3}{23 + 4y} = x$
$x = \frac{3}{23 + 4y}$
Now that both x's from both equation is alone,
all we need to do is to put them in one equation.

x from 1st equation=x from 2nd equation

$\frac{4}{14 - 3y} = \frac{3}{23 + 4y}$
$4(23 + 4y) = 3(14 - 3y)$
$92 + 16y = 42 - 9y$
$92 - 42 = - 9y - 16y$
$50 = - 25y$
$\frac{50}{ - 25} = y$
$y = - 2$
Now put y=-2 into any of the x equation
$x = \frac{4}{14 - 3( - 2)}$
$x = \frac{4}{20} = \frac{1}{5}$

Answer 2

Solution:-

4/x + 3y = 14........(1)
3/x - 4y =23...........(2)

multiply by in eq(1)×4 ans eq(2)×3 then

16/x+ 12y = 56..............(3)
9/x- 12y = 69................(4)
________________________add_________
25/x = 125
x = 1/5
puting value in eq (1)

20 + 3y = 14

3y = 14-20

y = -6/3

y= -2

(x,y) = ( 1/5, -2) ans