Parametric linear equations problems - easy

Solution:
If we can divide by a, there is always the solution . Let's check the case where we cannot divide by a, in other words a=0. We get the equation , which has no solutions. Therefore the answer to the problem is a=0.

Solution:
For an equation to have any x as solution, it must be of the form 0x=0. Which means that , or a=2.

Solution:
For any x, the value of the left side is zero. We get b-7=0, or b=7. By substituting, we get 0x=0, which has infinitely many solutions.

Solution:
We subtract a from both sides of the equation to get
. We substitute a=3:

Solution:
If the equation is to be not defined, then a denominator must be zero. The only denominator is , so we get

Solution:
We directly substitute:

Solution:
We substitute:

Solution:
We substitute:

Solution:
We directly substitute: