` ( 1 ) /(x) + (1 ) /( y) = 7`,
` ( 2)/(x) + ( 3) /( y) = 17 (x ne 0, y ne 0 )` .

Explanation

To solve the system of equations

\[ \frac{1}{x} + \frac{1}{y} = 7 \quad (1) \]
\[ \frac{2}{x} + \frac{3}{y} = 17 \quad (2) \]

we will use substitution to simplify the equations. Let's define:

\[ u = \frac{1}{x} \quad \text{and} \quad v = \frac{1}{y} \]

Now we can rewrite the equations in terms of \(u\) and \(v\):

1. From equation (1):
\[ u + v = 7 \quad (3) \]

2. From equation (2):
\[ 2u + 3v = 17 \quad (4) \]

### Step 1: Solve for one variable
From equation (3), we can express \(v\) in terms of \(u\):

\[ v = 7 - u \quad (5) \]

### Step 2: Substitute into the second equation
Now substitute equation (5) into equation (4):

\[ 2u + 3(7 - u) = 17 \]

### Step 3: Simplify and solve for \(u\)
Expanding the equation:

\[ 2u + 21 - 3u = 17 \]

Combine like terms:

\[ -1u + 21 = 17 \]

Subtract 21 from both sides:

\[ -u = 17 - 21 \]
\[ -u = -4 \]

Multiply by -1:

\[ u = 4 \quad (6) \]

### Step 4: Find \(v\)
Now substitute the value of \(u\) back into equation (5):

\[ v = 7 - 4 = 3 \quad (7) \]

### Step 5: Find \(x\) and \(y\)
Recall that \(u = \frac{1}{x}\) and \(v = \frac{1}{y}\). Therefore:

From equation (6):
\[ \frac{1}{x} = 4 \implies x = \frac{1}{4} \quad (8) \]

From equation (7):
\[ \frac{1}{y} = 3 \implies y = \frac{1}{3} \quad (9) \]

### Final Solution:
Thus, the solutions for \(x\) and \(y\) are:

\[ x = \frac{1}{4}, \quad y = \frac{1}{3} \]

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