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# How do I solve this using elimination?

+5
196
3

6x−y+3z = 28

5x−2y+2z = 28

−3x−y+4z = -17

Guest Feb 26, 2017
#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
+87301
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
#3
+19632
0

6x−y+3z = 28

5x−2y+2z = 28

−3x−y+4z = -17

heureka  Feb 27, 2017