#1**0 **

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**

Guest Feb 26, 2017

#2**0 **

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

CPhill
Feb 26, 2017