https://file.aiquickdraw.com/mathbot/file/17262762220764sfkpy5f.jpg

The equation in the image is:

\[
-3x - 5y = -2
\]

We are solving for \( y \) in terms of \( x \).

### Steps to solve for \( y \):
1. Start with the original equation:
   \[
   -3x - 5y = -2
   \]

2. Add \( 3x \) to both sides to isolate the \( y \)-term:
   \[
   -5y = 3x - 2
   \]

3. Divide both sides by \( -5 \) to solve for \( y \):
   \[
   y = \frac{3x - 2}{-5}
   \]

4. Simplify the expression:
   \[
   y = -\frac{3x}{5} + \frac{2}{5}
   \]

So, the solution for \( y \) is:

\[
y = -\frac{3x}{5} + \frac{2}{5}
\]

Would you like further details on how this was solved, or do you have any questions?

### Related questions:
1. How would the solution change if the equation was \( 3x + 5y = 2 \)?
2. How can you check if a solution is correct by plugging values of \( x \)?
3. What happens to the equation when \( x = 0 \)?
4. Can you solve this equation graphically, and what would the graph look like?
5. How would this problem change if the coefficients of \( x \) and \( y \) were different?

### Tip:
When solving linear equations, remember to keep track of negative signs when isolating variables.

Learn how to solve the linear equation -3x - 5y = -2 with a detailed step-by-step solution. This problem covers key algebraic concepts, including isolating variables and solving for y in terms of x. Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation