Question

For the given a and b, show that the equation ax = b does not have a solution for all possible b, and describe the set of all b for which ax = b does have a solution.

Answer 1

The equation ax = b has a solution only if a is not equal to zero; if a is zero, b must also be zero for there to be a solution.

Step-by-step explanation:

For the equation ax = b, there are situations where a solution does not exist for all values of b. The equation has a solution if and only if a is not equal to zero. When a = 0, the equation 0x = b does not have a solution unless b is also equal to zero. Therefore, the set of all b for which ax = b does have a solution, is the set of all real numbers if a is not zero. If a is zero, the only b that would satisfy the equation is b = 0.