In this topic, you will learn about 2 special cases that may be seen in different algebraic equations, which are infinitely many solutions and no solutions. While they may sound confusing and very strange, once we look at some examples, we can then see the logic behind them and how they can be reasoned out. For example, let's say we have an equation with the same coefficients in front of variables on each side, but other parts of the equation are different. In 3x+12=3x-9, we can see that while there is 3x on both sides, there is a 12 on the left side, while there is a -9 on the right, meaning that the constant terms are not equal. They are called constant terms because, as their name suggests, they are constant, meaning their numerical value never changes. Now, if we try to solve the equation as normal by subtracting all of the variables from one side, it would cancel on both sides, which would result in both 3x's cancelling out. That would result in 12=-9, which obviously is not a true statement, meaning that there would be no solution, because no matter what number you set as equal to x, it will result in a false statement. Now, let's look if the equation was exactly the same on both sides, such as with 2x+6=2x+6. In that case, when the x's cancel out, we would have 6=6, which is true. Therefore, no matter what number is set equal to x, they would be equal, due to being multiplied by 3 on both sides and added to 6, meaning that there would be infinitely many solutions. Now that you have a foundational concept, we can get into some more complex examples.