Final answer:
Upon comparing the coefficients of the system of equations, we observe an inconsistency that indicates these equations represent planes with no intersection points; hence, there is no solution to the system.
Step-by-step explanation:
The provided system of equations needs to be analyzed to determine if there is a unique solution, infinitely many solutions, or no solution at all. To do this, we can use algebraic methods such as substitution, elimination, or matrix operations. However, these equations can also be quickly assessed by comparing their coefficients.
Let us examine the equations closely:
- x + 2y + 3z = 1
- 2x + y + 3z = 2
- 5x + 5y + 9z = 4
Looking at the first two equations, if we multiply the first equation by 2, we'll have:
Comparing this with the second equation, we can see that the terms involving x and z are multiples, but the y-term is not, nor are the constants on the right-hand side equal. This inconsistency suggests that there is no solution for the system of equations, as they represent three planes that do not intersect at any common point.
Therefore, the correct answer is c. there is no solution.