To solve the system of equations 3x + 6y = 2 and 15x + 30y = 10, we can start by simplifying the second equation.
If we divide every term in the second equation by 5, we get:
3x + 6y = 2
This is exactly the same as the first equation, indicating that the two equations are dependent. In other words, both equations represent the same line on a graph.
Since both equations are the same, there are infinitely many solutions to this system. Any pair of (x, y) that satisfies 3x + 6y = 2 will be a solution. We can express y in terms of x to show this.
Rearranging the equation gives:
6y = 2 – 3x
y = (2 – 3x) / 6
This means for any value of x we choose, we can find a corresponding value of y, hence an infinite number of solutions exist.