https://file.aiquickdraw.com/mathbot/file/17288693160650usrp7m9.jpg

Let's analyze the system of linear equations from the image:

\[
x + y = 3 \tag{1}
\]
\[
x + y = 10 \tag{2}
\]

To solve this using substitution, we notice that both equations are identical in form, but their right-hand sides differ. Specifically:

From (1): 
\[
x + y = 3
\]

From (2): 
\[
x + y = 10
\]

These two equations contradict each other, because \(x + y\) cannot be both 3 and 10 at the same time. Therefore, this system has **no solution**. It is an inconsistent system of equations.

Would you like further clarification on this? 

Here are five related questions to consider:
1. What does it mean for a system of equations to be inconsistent?
2. How can substitution be applied in systems where solutions exist?
3. What happens in a system with infinite solutions?
4. Can graphical methods confirm the solution to this system?
5. What other methods, besides substitution, can be used to solve systems of linear equations?

**Tip:** When you encounter two equations with a contradiction like this, it indicates that the lines are parallel and never intersect, confirming that there is no solution.

Use the method of substitution to solve the system of linear equations: x + y = 3, x + y = 10.

Learn how to solve the system of linear equations using substitution. This problem features the system x + y = 3 and x + y = 10, showing that the system has no solution due to a contradiction. Suitable for students in Grades 8-10.

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