0 x+19 y-10 z = -75 | (equation 2)
0 x+0 y+z = -2 | (equation 3)
Add 10 × (equation 3) to equation 2:
{-(5 x)+4 y+5 z = -15 | (equation 1)
0 x+19 y+0 z = -95 | (equation 2)
0 x+0 y+z = -2 | (equation 3)
Divide equation 2 by 19:
{-(5 x)+4 y+5 z = -15 | (equation 1)
0 x+y+0 z = -5 | (equation 2)
0 x+0 y+z = -2 | (equation 3)
Subtract 4 × (equation 2) from equation 1:
{-(5 x)+0 y+5 z = 5 | (equation 1)
0 x+y+0 z = -5 | (equation 2)
0 x+0 y+z = -2 | (equation 3)
Subtract 5 × (equation 3) from equation 1:
{-(5 x)+0 y+0 z = 15 | (equation 1)
0 x+y+0 z = -5 | (equation 2)
0 x+0 y+z = -2 | (equation 3)
Divide equation 1 by -5:
{x+0 y+0 z = -3 | (equation 1)
0 x+y+0 z = -5 | (equation 2)
0 x+0 y+z = -2 | (equation 3)
Collect results:
Answer: |x = -3 y = -5 z = -2
+129840 x+3y-3z=-12 (1)
3x-3y-4z=14 (2)
-5x+4y+5z=-15 (3)
Add (1) and (2)
4x - 7z = 2 (4)
Multiply (1) by 4 and (3) by -3....this gives us
4x + 12y - 12z = -48
15x - 12y - 15z = 45 add these giving us
19x - 27z = -3 (5) multiplly (4) by 19 and (5) by -4 ....this gives us.....
76x - 133z = 38
-76x + 108z = 12 add these
-25z = 50 divide both sides by -25
z = - 2 and using (4) to find x, we have that 4x - 7(-2) = 2 → 4x + 14 = 2 → 4x = -12 → x = -3
And using (1) to find y, we have : -3 +3y-3(-2)=-12 → 3 + 3y = -12 → 3y = -15 → y = -5
