Solve for x and y
`(2)/(x)+(3)/(y)=2, (8)/(x)-(6)/(y)=2`

Answer

To solve the equations

\[ \frac{2}{x} + \frac{3}{y} = 2 \]

and

\[ \frac{8}{x} - \frac{6}{y} = 2, \]

we will use substitution. Let's follow the steps:

### Step 1: Substitute Variables
Let \( u = \frac{1}{x} \) and \( v = \frac{1}{y} \). Then we can rewrite the equations as:

1. \( 2u + 3v = 2 \) (Equation 1)
2. \( 8u - 6v = 2 \) (Equation 2)

### Step 2: Solve Equation 1 for \( u \)
From Equation 1, we can express \( u \) in terms of \( v \):

\[ 2u = 2 - 3v \]

Dividing both sides by 2 gives:

\[ u = 1 - \frac{3v}{2} \]

### Step 3: Substitute \( u \) in Equation 2
Now, we substitute the expression for \( u \) into Equation 2:

\[ 8(1 - \frac{3v}{2}) - 6v = 2 \]

Distributing the 8:

\[ 8 - 12v - 6v = 2 \]

Combine like terms:

\[ 8 - 18v = 2 \]

### Step 4: Solve for \( v \)
Now, isolate \( v \):

\[ -18v = 2 - 8 \]
\[ -18v = -6 \]

Dividing both sides by -18 gives:

\[ v = \frac{1}{3} \]

### Step 5: Substitute \( v \) back to find \( u \)
Now we substitute \( v \) back into the expression for \( u \):

\[ u = 1 - \frac{3 \cdot \frac{1}{3}}{2} \]
\[ u = 1 - \frac{1}{2} = \frac{1}{2} \]

### Step 6: Find \( x \) and \( y \)
Recall that \( u = \frac{1}{x} \) and \( v = \frac{1}{y} \):

1. From \( u = \frac{1}{2} \):
\[ \frac{1}{x} = \frac{1}{2} \implies x = 2 \]

2. From \( v = \frac{1}{3} \):
\[ \frac{1}{y} = \frac{1}{3} \implies y = 3 \]

### Final Answer
Thus, the solution is:

\[ x = 2, \quad y = 3 \]