2x-4y-z=8 . . . . . . . . (1)
3x+2y+z=11 . . . . . . (2)
5x-2y+3z=13 . . . . . .(3)
From (1), z = 2x - 4y - 8 . . . (4)
substituting for z in eqtns (2) and (3), we have
3x + 2y + 2x - 4y - 8 = 11 => 5x - 2y = 19 . . . (5)
5x - 2y + 3(2x - 4y - 8) = 13 => 5x - 2y + 6x - 12y - 24 = 13 => 11x - 14y = 37 . . .(6)
(5) x 7 => 35x - 14y = 133 . . . (7)
(6) - (7) => -24x = -96 => x = 4
From (5), 5(4) - 2y = 19 => 20 - 19 = 2y => y = 1/2
From (1), 2(4) - 4(1/2) - z = 8 => 8 - 2 - z = 8 => z = 6 - 8 = -2
Therefore, x = 4; y = 1/2; and z = -2
