https://file.aiquickdraw.com/mathbot/file/1726689384753pb1qgisy.jpg

The equation in the image is given as:

\[
\frac{8}{x} + \frac{5}{y} = \frac{10}{5x}
\]

We are asked to solve for \( y \). Let's go step by step:

1. Simplify the right-hand side:

\[
\frac{10}{5x} = \frac{2}{x}
\]

So, the equation becomes:

\[
\frac{8}{x} + \frac{5}{y} = \frac{2}{x}
\]

2. Subtract \(\frac{8}{x}\) from both sides to isolate \(\frac{5}{y}\):

\[
\frac{5}{y} = \frac{2}{x} - \frac{8}{x}
\]

\[
\frac{5}{y} = \frac{2 - 8}{x}
\]

\[
\frac{5}{y} = \frac{-6}{x}
\]

3. Now, solve for \( y \) by multiplying both sides by \( y \) and then dividing by \( -6/x \):

\[
y = \frac{5x}{-6}
\]

\[
y = -\frac{5x}{6}
\]

Thus, the solution for \( y \) is \( y = -0.83x \).

### Answer: \(-0.83x\)

Would you like any further explanation?

### Related questions:
1. How do you solve equations with fractions?
2. What are the steps to isolate a variable in an equation?
3. How do you simplify complex fractions?
4. What is the importance of balancing both sides of an equation?
5. How can you check your solution for an equation?

### Tip: Always simplify the equation as much as possible before solving for a variable.

Solution of the equation 8/x + 5/y = 10/5x for y.

Learn how to solve the equation 8/x + 5/y = 10/5x for y. This problem involves algebraic manipulation and fraction operations. Step-by-step explanation with formulas and relevant theorems. Suitable for students in Grades 9-11.

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