Find all values of and such that the system is 1. inconsistent; 2. consistent with exactly one solution; 3. consistent with infinitely many solutions. - ax1 - x2 = 3 1-2x1 + 4x2 = 6b.

If - 4a - 2 = 0. a = - 1/2 and b other than - 11/6 the system is inconsistent.

If - 4a - 2 = 0. a = - 1/2 and b = - 11/6 the system is consistent with infinite solutions.

If a is other than - 1/2 the system is consistent with only one solution

Step-by-step explanation:

An inconsistent system is one that has no solutions.

An consistent system is one that has at least one solution.

Det (system) = (-4a - 2); Det (X1) = (13 - 6b); Det (X2) = (a - 6ab + 6)

If - 4a - 2 = 0. a = - 1/2 and b other than - 11/6 the system is inconsistent.

If - 4a - 2 = 0. a = - 1/2 and b = - 11/6 the system is consistent with infinite solutions.

If a is other than - 1/2 the system is consistent with only one solution