Let's solve the equation:

Given:  
\[
\frac{5}{3} = -x - \frac{5}{3}y
\]

### Step 1: Move the variables to one side

We add \( x \) and \(\frac{5}{3}y \) to both sides to isolate them:

\[
x + \frac{5}{3}y + \frac{5}{3} = 0
\]

### Step 2: Express \( x \) in terms of \( y \)

Next, subtract \(\frac{5}{3}y\) from both sides:

\[
x + \frac{5}{3} = -\frac{5}{3}y
\]

Now, subtract \(\frac{5}{3}\) from both sides to solve for \( x \):

\[
x = -\frac{5}{3}y - \frac{5}{3}
\]

This gives the equation:
\[
x = -\frac{5}{3}(y + 1)
\]

Let me know if you want any clarification!

Here are 5 questions related to this topic:
1. How do you graph a linear equation in two variables?
2. What is the general form of a linear equation?
3. How can you solve for \( y \) instead of \( x \) in this equation?
4. What is the slope of this equation if graphed?
5. How do you determine the intercepts from an equation?

**Tip:** When solving linear equations, always aim to isolate the variable you need by moving terms across the equation systematically.

Learn how to solve the linear equation 5/3 = -x - 5/3 y with a detailed step-by-step explanation. This problem focuses on algebraic techniques, including moving terms and solving for x in terms of y. Suitable for students in Grades 8-10.

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