Question 914130
how to solve ordered triple as 6x+2y-3z=-17 7x-5y+z=72 2x+8y+3z=-21
<pre>
{{{system (6x + 2y - 3z = - 17______eq_(i), 7x - 5y +  z =   72_________eq_ (ii), 2x + 8y + 3z = - 21______eq_(iii))}}}
 8x + 10y = - 38 ---------- Adding eqs (i) & (iii) to eliminate z ----- eq (iv)
 21x - 15y + 3z = 216 ----- Multiplying eq (ii) by 3 ------ eq (v)
 27x - 13y  =   199 ------- Adding eqs (v) & (i) ---------- eq (vi)
270x - 130y =  1,990 ------ Multiplying eq (vi) by 10 ----- eq (vii)
104x + 130y =  - 494 ------ Multiplying eq (iv) by 13 ----- eq (viii)
374x = 1,496 ------ Adding eqs (vii) & (viii)
x = {{{1496/374}}}, or {{{highlight_green(4)}}}

8(4) + 10y = - 38 ------- Substituting 4 for x in eq (iv)
32 + 10y = - 38
10y = - 38 - 32
10y = - 70
y = {{{(- 70)/10}}}, or {{{highlight_green(- 7)}}}

6(4) + 2(- 7) - 3z = - 17 ------- Substituting 4 for x and - 7 for y in eq (i)
24 - 14 - 3z = - 17
10 - 3z = - 17
- 3z = - 17 - 10
- 3z = - 27
z = {{{(- 27)/(- 3)}}}, or {{{highlight_green(9)}}}