The system of linear equations presented in the image is:

1. $2x + y - 3 = 0$
2. $4x + 2y = 12$

Step-by-step solution:

1. Rewrite the equations:

• From the first equation: $2x + y = 3 \quad \text{(move 3 to the other side)}$

  So the system becomes: $2x + y = 3 \quad \text{(Equation 1)}$ $4x + 2y = 12 \quad \text{(Equation 2)}$

2. Solve by substitution or elimination:

Let's use the substitution method by solving for $y$ in Equation 1: $y = 3 - 2x$

3. Substitute this into Equation 2:

$4x + 2(3 - 2x) = 12$ Simplifying: $4x + 6 - 4x = 12$ $6 = 12$ This leads to a contradiction, which means there is no solution to this system. The lines are parallel and never intersect.

Thus, the system of equations is inconsistent, and there is no solution.

Would you like any further details or clarification on this?

Here are five related questions to consider:

1. What does it mean when two lines are parallel in terms of their slopes?
2. How would the solution change if the system had been consistent?
3. Can graphing these equations visually demonstrate that they are parallel?
4. What is the geometrical interpretation of an inconsistent system?
5. How can you solve other systems of equations using the elimination method?

Tip: If you reach a contradiction like $6 = 12$, it typically indicates that the system of equations is inconsistent, meaning no solution exists.