#### Answer

The answers are below.

#### Work Step by Step

a)
We first simplify by letting $v=1/x$ and $u = 1/y$. Then, we multiply by the necessary value to make a variable cancel and solve. Finally, we plug the value of the variable we found in order to find the missing variable.
$v + 2u = 7/12 \\ 3v - 2u = 5/12 $
Thus:
$ 4v = 1 \\ v = .25 $
And:
$ u = 1/6$
Thus, x=4 and y=6.
b)
We first simplify by letting $v=1/x$ and $u = 1/y$. Then, we multiply by the necessary value to make a variable cancel and solve. Finally, we plug the value of the variable we found in order to find the missing variable.
$2v + 3u = 19/15 \\ -2v + u = -7/15 $
Thus:
$ 4u = 12/15 \\u = 1/5 $
And:
$ v = 1/3$
Thus, x=3 and y=5.
c)
We first simplify by letting $v=1/x$ and $u = 1/y$. Then, we multiply by the necessary value to make a variable cancel and solve. Finally, we plug the value of the variable we found in order to find the missing variable.
$3v - 2u = 13/6 \\ 2v + 3u = 0 $
Thus:
$ -13u = 13/3 \\ u =-1/3$
And:
$ v = 1/2$
Thus, x=2 and y=-3.
d)
We first simplify by letting $v=1/x$ and $u = 1/y$. Then, we multiply by the necessary value to make a variable cancel and solve. Finally, we plug the value of the variable we found in order to find the missing variable.
$4v + u = 11 \\ 3v -5u = -9 $
Thus:
$ 23v = 46 \\ v = 2 $
And:
$ u = 3$
Thus, x=1/2 and y=1/3.
e)
We first simplify by letting $v=1/x$ and $u = 1/y$. Then, we multiply by the necessary value to make a variable cancel and solve. Finally, we plug the value of the variable we found in order to find the missing variable.
$5v - 2u = 23 \\ 4v + 3u = 23/2 $
Thus:
$ 23v = 92 \\ v = 4 $
And:
$ u = -3/2$
Thus, x=1/4 and y=-2/3.
f)
We first simplify by letting $v=1/x$ and $u = 1/y$. Then, we multiply by the necessary value to make a variable cancel and solve. Finally, we plug the value of the variable we found in order to find the missing variable.
$2v - 7u = 9/10 \\ 5v + 4u = -41/20 $
Thus:
$ -43u = 8.6 \\ u = -1/5 $
And:
$ v = -1/4$
Thus, x=-4 and y=-5.