https://file.aiquickdraw.com/mathbot/file/1729091546847tz7ucz2f.jpg

The system of equations presented is:

\[
y = -3x + 1
\]
\[
2y = -6x + 2
\]

### Step-by-Step Solution:

1. **Simplify the second equation:**

   Start by simplifying the second equation to check if it's related to the first one. Divide the second equation by 2:

   \[
   y = -3x + 1
   \]

   This is identical to the first equation.

2. **Analyze the system:**

   Since both equations are equivalent, they represent the same line. This means:
   
   - The system has infinitely many solutions because both equations describe the same line.
   - The system is **consistent** (since there is a solution).
   - The system is **dependent** (because the equations are identical and do not represent two distinct lines).

### Conclusion:

The system of equations is **consistent and dependent**.

Would you like more details or have any further questions?

Here are 5 relative questions based on this problem:

1. What does it mean for a system of equations to be inconsistent?
2. Can a system of two linear equations ever be consistent and independent if their slopes are equal?
3. How would you solve a system of equations graphically?
4. How do you check if a system of equations is independent?
5. What are the implications of having a dependent system in practical scenarios?

**Tip:** A system is dependent when both equations describe the same line, meaning all solutions of one are also solutions of the other.

Is the system of equations consistent and independent, consistent and dependent, or inconsistent? The equations are: y = -3x + 1 and 2y = -6x + 2.

Analyze whether the system of equations y = -3x + 1 and 2y = -6x + 2 is consistent and dependent or independent. Learn the step-by-step solution by simplifying and comparing the equations. Ideal for 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