To solve the equation:

\[
\frac{1}{x} + \frac{1}{y} = \frac{7}{10}
\]

We can follow these steps:

### Step 1: Find a common denominator for the left-hand side
The left-hand side is:

\[
\frac{1}{x} + \frac{1}{y} = \frac{x + y}{xy}
\]

### Step 2: Set the equation equal to the right-hand side
Now we have:

\[
\frac{x + y}{xy} = \frac{7}{10}
\]

### Step 3: Cross-multiply to eliminate the fractions
Cross-multiplying gives:

\[
10(x + y) = 7xy
\]

### Step 4: Rearrange the equation
Rearrange the equation to group terms:

\[
7xy - 10x - 10y = 0
\]

### Step 5: Factor the equation
To solve for \(x\) and \(y\), you can use techniques like substitution, factoring, or using special methods for solving systems of equations, but this equation doesn't factor neatly.

Would you like to solve for specific values of \(x\) and \(y\), or do you want a deeper explanation on how to handle this? 

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Here are 5 related questions to practice:

1. Solve \(\frac{1}{a} + \frac{1}{b} = \frac{3}{5}\).
2. What is the solution for \(\frac{2}{x} + \frac{1}{y} = 1\)?
3. Solve the equation \(\frac{1}{x} - \frac{1}{y} = \frac{2}{3}\).
4. How do you solve systems of equations involving fractions?
5. Find two numbers \(x\) and \(y\) such that \(\frac{1}{x} + \frac{1}{y} = 1\).

**Tip:** Cross-multiplying is a useful technique to eliminate fractions in equations!

Learn how to solve the equation 1/x + 1/y = 7/10 by using cross-multiplication. This detailed guide explains key algebraic concepts and the cross-multiplication theorem, suitable for students in Grades 8-10.

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