Question

Determine all possibilities for the solution set of the system of 2 equations in 3 unknowns that has x1 = 4, x2 = −7, x3 = 0 as a solution.

(a) one or finitely many

(b) infinite

(c) finite

(d) zero

I had been asked this question during an internship interview.

Question is taken from Counting topic in chapter Counting of Discrete Mathematics

Answer 1

Correct choice is (b) infinite

For explanation I would say: Since m1 = 4, x2 = −7, x3 = 0 is a solution of the system, the system is not inconsistent. Thus the only possibility is infinitely many solutions.