Question 1027945

Please help me solve the following for x, y, and z. and please show the work.

3x+2y+z=8
2x-3y+2z=-16
x+4y-z=20
<pre>3x + 2y +  z =    8 ------ eq (i)
2x – 3y + 2z = - 16 ------ eq (ii)
 x + 4y –  z =   20 ------ eq (iii)
4x + 6y = 28 ---------- Adding eqs (i) & (iii) ------- eq (iv)
2x + 8y – 2z = 40 ----- Multiplying eq (iii) by 2 ---- eq (v)
4x + 5y = 24 ---------- Adding eqs (v) & (ii) -------- eq (vi)
{{{highlight_green(y = 4)}}} -------- Subtracting eq (vi) from eq (iv)

4x + 6(4) = 28 -------- Substituting 4 for y in eq (iv)
4x + 24 = 28
4x = 4
x = {{{4/4}}}, or {{{highlight_green(x = 1)}}}

1 + 4(4) – z = 20 --------- Substituting 1 for x and 4 for y in eq (iii)
1 + 16 – z = 20
17 – z = 20
- z = 20 – 17
z = {{{3/(- 1)}}}, or {{{highlight_green(z = - 3)}}}