Solve the system X 2y 5z 8 2x y 2z 6 Select the correc

Solve the system. X - 2y + 5z = 8 2x - y + 2z = 6 Select the correct choice below and fill in any answer boxes with (Simplify your answers.) A. There is one solution. The solution set is B. There are infinitely many solutions. The solution set is C. There are infinitely many solutions. The solution set is D. The solution set is the empty set.

Solution

given x-2y +5z =8,2x-y +2z =6

x-2y +5z -2*(2x-y +2z)=8 -2*6

=>x-2y +5z -4x+2y -4z=8 -12

=>-3x+z=-4

=>z=3x-4

x-2y +5z =8, z=3x-4

=> x-2y +5(3x-4) =8

=> x-2y +15x-20 =8

=> 2y= 16x-28

=> y= 8x-14

there are infintely many soolutions . the solution set is {(x,8x-14,3x-4)}