Divide equation 3 by 43:
{6 x - y + 3 z = 28 | (equation 1)
0 x - 7 y - 3 z = 28 | (equation 2)
0 x+0 y+z = (-63)/43 | (equation 3)
Add 3 × (equation 3) to equation 2:
{6 x - y + 3 z = 28 | (equation 1)
0 x - 7 y+0 z = 1015/43 | (equation 2)
0 x+0 y+z = -63/43 | (equation 3)
Divide equation 2 by -7:
{6 x - y + 3 z = 28 | (equation 1)
0 x+y+0 z = (-145)/43 | (equation 2)
0 x+0 y+z = -63/43 | (equation 3)
Add equation 2 to equation 1:
{6 x + 0 y+3 z = 1059/43 | (equation 1)
0 x+y+0 z = -145/43 | (equation 2)
0 x+0 y+z = -63/43 | (equation 3)
Subtract 3 × (equation 3) from equation 1:
{6 x+0 y+0 z = 1248/43 | (equation 1)
0 x+y+0 z = -145/43 | (equation 2)
0 x+0 y+z = -63/43 | (equation 3)
Divide equation 1 by 6:
{x+0 y+0 z = 208/43 | (equation 1)
0 x+y+0 z = -145/43 | (equation 2)
0 x+0 y+z = -63/43 | (equation 3)
Collect results:
Answer: |x = 208/43 y = -145/43 z = -63/43
+128406 6x−y+3z = 28 (1)
5x−2y+2z = 28 (2)
−3x−y+4z = -17 (3)
Multiply (1) by -2......add to (2) and we have
-7x - 4z = - 28 (3)
Multiply (3) by -2......add to (2) and we have
11x - 6z = 62 (4)
Multiply (3) by -6 and (4) by 4
42x + 24z = 168
44x - 24z = 248 add these
86x = 416 divide both sides by 86
x = 416/86 = 208/43
Using (4) to find z, we have
11(208/43) - 6z = 62
2288/43 - 62*43/43 = 6z
-378 /(6 *43) = z
-63/43 = z
And using (1) to find y
6x−y+3z = 28
y = 6x + 3z -28
y = 6(208/43) + 3(-63/43) -[28 *43] / 43
y = -145/43
