Question

If 2/x+ 3/y =13 and 5/x- 4/y = -2, then x+y equals

Answer 1

Answer:

$x + y = \frac{5}{6}$

Step-by-step explanation:

Let:

$u = \frac{1}{x} \\ v = \frac{1}{y}$

This allows us to manipulate the equations like we normally would.

$2u + 3v = 13 \\ 5u - 4v = - 2 \\ \\ + 8u + 12v = 52 \\ + 15u - 12v = - 6 \\ 23u = 46 \\ u = 2 \\ \\ 2(2) + 3v = 13 \\ 4 + 3v = 13 \\ 3v = 9 \\ v = 3$

Then, we return the values where they belong.

$u = \frac{1}{x} \\ 2 = \frac{1}{x} \\ x = \frac{1}{2} \\ \\ v = \frac{1}{y} \\ 3 = \frac{1}{y} \\ y = \frac{1}{3}$

Finally, we add:

$\frac{1}{2} + \frac{1}{3} = \frac{3}{6} + \frac{2}{6} = \frac{5}{6}$