The system x+4y-2z=3, 3x+y+5z=7, 2x+3y+z=5 has:

Question

The system x+4y-2z=3, 3x+y+5z=7, 2x+3y+z=5 has: (A) infinite number of solutions (B) unique solution (C) trivial solution (D) no solution

Tardigrade Admin · Accepted Answer

Given system of equations are x+4y-2z=3 3x+y+5z=7 2x+3y+z=5 ∴ Δ =| beginmatrix 1 4 -2 3 1 5 2 3 1 endmatrix | =1(1-15)-4(3-10)-2(9-2) =-14+28-14=0 Since, Δ =0 and Δ 2≠ 0 ∴ No solution will exist.

Q. The system $x + 4 y - 2 z = 3,$ $3 x + y + 5 z = 7,$ $2 x + 3 y + z = 5$ has:

infinite number of solutions

unique solution

trivial solution

no solution

multiple solutions

Given system of equations are $x + 4 y - 2 z = 3$ $3 x + y + 5 z = 7$ $2 x + 3 y + z = 5$ $∴$ $Δ = ∣ ∣ 132413 - 2 51 ∣ ∣$ $= 1 (1 - 15) - 4 (3 - 10) - 2 (9 - 2)$ $= - 14 + 28 - 14 = 0$ Since, $Δ = 0$ and $Δ_{2} \neq = 0$ $∴$ No solution will exist.

Q. The system x+4y−2z=3, 3x+y+5z=7, 2x+3y+z=5 has: