For the system of linear equations: x + y + z = 6 α x + β y + 7z = 3 x + 2y + 3z = 14 Which of the following i…

Question

For the system of linear equations:
$$x + y + z = 6$$
$$\alpha x + \beta y + 7z = 3$$
$$x + 2y + 3z = 14$$
Which of the following is NOT true?

Accepted Answer

D. For every point $$(\alpha, \beta) 
eq (7, 7)$$ on the line $$x - 2y + 7 = 0$$, the system has infinitely many solutions.

Answer

A. If $$\alpha = \beta = 7$$, then the system has no solution

Answer

B. If $$\alpha = \beta$$ and $$\alpha 
eq 7$$, then the system has a unique solution.

Answer

C. There is a unique point $$(\alpha, \beta)$$ on the line $$x + 2y + 18 = 0$$ for which the system has infinitely many solutions.

Answer & step-by-step solution