Final answer:
The given system of equations has an infinite number of solutions because the two equations represent the same line, forming a dependent system.
Step-by-step explanation:
The system of equations given is:
- 4x + 10y = 20
- 6x + 15y = 30
To determine the number of solutions for these equations, we need to analyze them to see if they are equivalent, parallel, or intersecting.
By dividing the first equation by 2, we get:
By dividing the second equation by 3, we get:
These transformed equations are identical, which tells us that the original equations are also equivalent. This means they represent the same line and therefore have an infinite number of solutions.
This is a case of a dependent system where all the points on the line represented by these equations satisfy both equations.