Question

The system of equations has unique solution,the find the solution set
2x+y+z=2
x+3y-z=5
3x+y-2z=6

Answer 1

Answer:

x = 1

y = 1

z = -1

Step-by-step explanation:

given

$2x + y + z = 2..... (1)\\ x + 3y - z = 5....(2) \\ 3x + y - 2z = 6....(3) \\ multiply \: eq \: (2) \: with \: 2 \\ 2x + 6y - 2z = 10.....(4) \\ eq \: (4) - (3) \\ (2x + 6y - 2z = 10) - (3x + y - 2z = 6) \\ 5y - x = 4 \\ x = 5y - 4......(5) \\ from \: eq \: (1) + (2) \\ (2x + y + z = 2) + (x + 3y - z = 5) \\ 3x + 4y = 7</p><p>put \: value \: of \: x \: from \: eq \: 5 \\ 3(5y - 4) + 4y = 7 \\ 15y - 12 + 4y = 7 \\ 19y = 19 \\ y = 1......(6) \\ {put \: value \: of \: y \: in \: eq \: 5} \\ x = 5y - 4 \\ x = 5 - 4 \\ x = 1 \\ {put \: the \: value \: of \: x \: and \: y \: in \: eq \: 1} \\ 2x + y + z = 2 \\ 2 + 1 + z = 2 \\ z = 2 - 3 \\ z = - 1$