Solve the system of linear equations and check any solutions algebraically.

Step-by-step explanation:

Hello,

   (1) 2x + 4y + z = 3

   (2) x - 2y - 3z = 4

   (3) x + y - z = -1

From (3) we can write z = x + y + 1 and we replace in (1)

2x + 4y + x + y + 1 = 3 <=> 3x + 5y = 3-1 =2

   (1') 3x + 5y = 2

and we replace in (2)

x - 2y -3(x+y+1) = 4 <=> -2x -5y -3 = 4 <=> -2x -5y = 4 + 3 = 7

   (2') -2x - 5y = 7

(1') + (2') gives

3x - 2x + 5y - 5y = 2 + 7 = 9

x = 9

we replace in (1')

3*9 + 5y = 2 <=> 27 + 5y = 2 <=> 5y = 2-27 = -25 <=> y = -25/5 = -5

y = -5

and then in (3)

9 - 5 - z = -1 <=> 4 - z = -1 <=> z = 4 + 1 = 5

z = 5

hope this helps

work is shown and pictured