The two equations that form a system with infinite solutions are:
2x - y = 3
4x - 2y = 6
To solve these equations, we can manipulate the first equation by multiplying both sides by 2 to get:
4x - 2y = 6
This is the same as the second equation, which means that they are equivalent. This means that every point on the line defined by these equations is a solution to the system. Therefore, there are infinite solutions to this system of equations.
To demonstrate this, we can plug in a couple of points into the original equations:
For example, let's try the point (1, -1):
2(1) - (-1) = 3
4(1) - 2(-1) = 6
Both equations are satisfied. Now let's try another point, such as (2, -1):
2(2) - (-1) = 3
4(2) - 2(-1) = 6
Again, both equations are satisfied. This demonstrates that there are multiple solutions to this system of equations.
In conclusion, when two equations are equivalent in a system, it means that every point on the line defined by these equations is a solution to the system. This results in infinite solutions to the system.