Final answer:
The given system of equations represents the same line and is therefore dependent with infinitely many solutions, represented by y = (10/3) - x.
Step-by-step explanation:
To solve the system of equations, let's first analyze the given equations:
- 3x + 3y = 10
- -9x - 9y = -30
By observing the second equation, it is clear that it is a multiple of the first. Specifically, if we multiply the first equation by -3, we get the second equation, as follows:
Multiplying the first equation by -3:
-3(3x + 3y) = -3(10)
-9x - 9y = -30
This tells us that the two equations are actually the same line; they are proportional to each other. Therefore, there isn't a unique solution to this system. Instead, any point on the line 3x + 3y = 10 will also satisfy the second equation.
The system is said to be dependent and has infinitely many solutions.
We can express the solution by solving the first equation for y:
3x + 3y = 10
3y = 10 - 3x
y = (10/3) - x
So the solution can be represented by the set of all points (x, y) where y equals (10/3) - x.