The system of equations x + 2y + 3z = 4, 2x + 3y + 4z \= 5,... | MATH - SYSTEM OF LINEAR EQUATIONS, SOME SPECIAL DETERMINANTS | SolveeIt | Solveeit

Today, October 3

Question

The system of equations x + 2y + 3z = 4, 2x + 3y + 4z

= 5, 3x + 4y + 5z = 6 has

A

Infinitely many solutions

B

No solution

C

A unique solution

D

None of these

Answer

Infinitely many solutions

Explanation

Solution

Since $\Delta = \left| \begin{matrix} 1 & 2 & 3 \\ 2 & 3 & 4 \\ 3 & 4 & 5 \end{matrix} \right| = 0$ , (row are in AP with common

difference 1)

Similarly ∆_x = ∆_y = ∆_z = 0