Expert: Sherman D. - 11/26/2008

Question
x+2y=12
3y-4z=25
x+6y+=20






9a+7b=-30
8b+5c=11
-3a+10c=73





2r+3s-4t=20
4r-s+5t=13
3r+2s+4t=15







x+y+Z=12
6X-2Y-Z=16
3X+4y+2z=28

Answer
9a + 7b = -30
8b + 5c = 11
-3a + 10c = 73

9a + 7b = -30
9a = -7b - 30
a = (-7/9)b - (10/3)

-3((-7/9)b - (10/3)) + 10c = 73
(7/3)b + 10 + 10c = 73
(7/3)b + 10c = 63
7b + 30c = 180

8b + 5c = 11
7b + 30c = 189

Multiply by top by -6

-48b - 30c = -66
7b + 30c = 189

-41b = 123
b = -3

a = (-7/9)(-3) - (10/3)
a = (7/3) - (10/3)
a = (-3/3)
a = -1

-3a + 10c = 73
-3(-1) + 10c = 73
3 + 10c = 73
10c = 70
c = 7

a = -1
b = -3
c = 7

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2r + 3s - 4t = 20
4r - s + 5t = 13
3r + 2s + 4t = 15

4r - s + 5t = 13
3r + 2s + 4t = 15

multiply top by 2

8r - 2s + 10t = 26
3r + 2s + 4t = 15

11r + 14t = 41

11r = -14t + 41
r = (-14/11)t + (41/11)

2r + 3s - 4t = 20
2((-14/11)t + (41/11)) + 3s - 4t = 20
(-28/11)t + (82/11) + 3s - 4t = 20
-28t + 82 + 33s - 44t = 220
33s = 72t + 138
s = (24/11)t + (46/11)

3r + 2s + 4t = 15

3((-14/11)t + (41/11)) + 2((24/11)t + (46/11)) + 4t = 15
(-42/11)t + (123/11) + (48/11)t + (92/11) + 4t = 15
(6/11)t + (215/11) + 4t = 15
6t + 215 + 44t = 165
50t = -50
t = -1

s = (24/11)t + (46/11)
s = (24/11)(-1) + (46/11)
s = (-24/11) + (46/11)
s = (22/11)
s = 2

r = (-14/11)t + (41/11)
r = (-14/11)(-1) + (41/11)
r = (14/11) + (41/11)
r = (55/11)
r = 5

r = 5
s = 2
t = -1

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x + y + z = 12
6x - 2y - z = 16
3x + 4y + 2z = 28

6x - 2y - z = 16
3x + 4y + 2z = 28

Multiply top by 2

12x - 4y - 2z = 32
3x + 4y + 2z = 28

15x = 60
x = 4

x + y + z = 12
4 + y + z = 12
y + z = 8
z = -y + 8

3x + 4y + 2z = 28
3(4) + 4y + 2(-y + 8) = 28
12 + 4y - 2y + 16 = 28
2y = 0
y = 0

z = -(0) + 8
z = 8

x = 4
y = 0
z = 8

your going to have to correct the first one.

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