Consistency of Equations:
To determine the consistency of the given system of equations, we need to check if they intersect at a single point, multiple points, or no point at all.

Graphical Solution:
- Plot the two equations on a graph to determine if they intersect at a single point.
- The first equation is 2x + 5y = 11, and the second equation is 4x + 10y = 22.
- By plotting these equations, if they intersect at a single point, the system is consistent and has a unique solution.

Algebraic Solution:
- To solve the system algebraically, we can use the method of substitution or elimination.
- Given equations are:
1. 2x + 5y = 11
2. 4x + 10y = 22
- Multiply the first equation by 2 to make the coefficients of x equal:
3. 4x + 10y = 22
- Now, compare this equation with the second equation:
4x + 10y = 22
- The equations are the same, indicating that they represent the same line.
- Therefore, the system of equations is consistent and has infinitely many solutions.

Conclusion:
- The system of equations is consistent and has infinitely many solutions as the equations represent the same line.
- The graphical representation also confirms that the two equations intersect at multiple points.
- Thus, the solution to the given system of equations is that they are consistent and have infinitely many solutions.