Question

Solve the following system of equations. X+ y+ z- w = 4 3x + y- z+ w = 10 x- 4y + 32+ w = -5 -x- y+ 2+ 4w = 4 Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. O A. There is one solution. The solution is ). (Type integers or simplified fractions.) O B. There are infinitely many solutions. The solutions are ( (Type integers or simplified fractions.) OC. There is no solution. W)

Answer 1

Sol Giveni xty + z-we4 3rty-the 10 x-4y +3z+wers - n- 4+2+ 4wr4 in augmented matrix for y Writing 11 - 4 -1 -1 Apply Ray R2-3R lo 3 - 1 4 R3 R3-R, Ry Ruth Os - 2 - 9 0 - 2 - 4 4 0 -5 2 2 0 0 2 3 Apply Rzy 2R3-5R2, 0 o o - 2 - 4 o 24 o 2 4 -16 3

Apply R3 R3) 8 R₂ - R2/2 8 0 +2 2 - 2 11 0 0 3 - 2 - 1 0 2 3 Apply Rz 3R3-222 1 I 1 - 1 1 2 -2 1 0 0 3 - 2 - Co o 0 13 26 13w226 3z-zwe-1 32 -4 - 1 3ze 3 1 & + 2z-Zwei y+2-42 aty +z-Wep. x+3+1- 2 4 xe 2) There is one solution, the solution is (2, 3, 12) Ang