The system of equations provided in the image is:

$3x + 2y = 7$ $3x + 2y = 4$

Step-by-Step Solution:

1. Examine the equations: Both equations have the same left-hand side, $3x + 2y$, but different right-hand sides (7 and 4). This indicates an inconsistency.

2. Subtract the equations: Subtract the second equation from the first: $(3x + 2y) - (3x + 2y) = 7 - 4$ This simplifies to: $0 = 3$

3. Conclusion: The result, $0 = 3$, is a contradiction. This means the system of equations has no solution and is inconsistent.

Key Takeaway:

The two equations represent parallel lines in the coordinate plane that never intersect, so there is no solution to this system.

Would you like further clarification or help understanding this concept? 😊

Here are 5 related questions to explore:

1. What does it mean for two lines to be parallel in a system of linear equations?
2. How can we graphically verify whether a system of equations is inconsistent?
3. How would we solve a system of equations that is consistent using elimination or substitution?
4. Can inconsistent systems occur with nonlinear equations? If so, how do we detect them?
5. What happens if the coefficients of $x$ and $y$ are proportional but the constants are not?

Tip: Always check for inconsistencies when two equations have identical left-hand sides but different right-hand sides. This often signals parallel lines with no intersection.