+0

# How do I solve this using elimination?

+5
148
3

6x−y+3z = 28

5x−2y+2z = 28

−3x−y+4z = -17

Guest Feb 26, 2017
Sort:

#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
+84354
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
+19095
0

6x−y+3z = 28

5x−2y+2z = 28

−3x−y+4z = -17

heureka  Feb 27, 2017

### 31 Online Users

We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details