The system 



   
 
4 6 8
2 3 8
x y
x y
is a/an _____________ system.

The given system of equations is:

\[
\begin{aligned}
    2x - 3y &= 8 \\
    4x + 6y &= -8
\end{aligned}
\]

This is a **dependent system** of linear equations because both equations represent the same line. To see this, you can multiply the first equation by 2, and you'll get the second equation:

\[
\begin{aligned}
    2(2x - 3y) &= 2(8) \\
    4x - 6y &= 16
\end{aligned}
\]

But the second equation is \( 4x + 6y = -8 \), so these two equations represent parallel lines that never intersect, meaning that the system is inconsistent, and they are contradictory, implying **no solution**.

Thus, the system is **inconsistent**.

Would you like more details or further clarification?

Here are 5 related questions you might explore:
1. How do you classify systems of equations as dependent, independent, or inconsistent?
2. What is the graphical interpretation of an inconsistent system?
3. What is the difference between dependent and inconsistent systems?
4. How do you solve a system of equations by substitution?
5. What are the methods to determine if a system is consistent or inconsistent?

**Tip:** When solving a system of linear equations, try to simplify or multiply the equations to check if one is a multiple of the other—this often reveals the nature of the system.

The system 
2x - 3y = 8
4x + 6y = -8
is a/an _____________ system.

Explore how to identify and solve an inconsistent system of linear equations like 2x - 3y = 8 and 4x + 6y = -8. This problem highlights key concepts in algebra, including the classification of systems of equations and their solutions. Ideal for students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation