Question

2x+y+z= - 2
3x-2y-2z= -3
-5x + 3y+4z=7

Solve the system algebraically and check..

someone can help me here i will give medals and im gonna be your fan

Answer 1

@Callisto

Answer 2

@shinalcantara

Answer 3

can anyone can help me :D

Answer 4

please help me guys.. we will have an exam tommorow i need to solve this

Answer 5

largely donkey work, i would get a computer to do it
http://www.wolframalpha.com/input/?i=2x%2By%2Bz%3D-2+and+3x-2y-2z%3D-3++and+-5x+%2B+3y%2B4z%3D7

Answer 6

but if course this will not help you on a test
lets see if we can eliminate one of the variables
\[3x-2y-2z= -3 \\-5x + 3y+4z=7\] multiply the first one by 2 and get
\[6x-4y-4z= -6\\ -5x + 3y+4z=7\] which after adding gets
\[x-y=1\]

Answer 7

repeat with \[2x+y+z= - 2\\ 3x-2y-2z= -3\][ again multiply the first one by 2 and get
\[4x+2y+2z= - 4\\ 3x-2y-2z= -3\] adding gets \[7x=-7\] making \(x=1\)

Answer 8

ok that was wrong
\[7x=-7\\
x=-1\]

Answer 9

ok

Answer 10

now that you know \(x=-1\) and \(x-y=1\) that tells you \(y=-2\)

Answer 11

replace \(x\)by \(-1\) and \(y\) by \(-2\) in any of the three equations to find that \(z=2\)

Answer 12

2x + y + z= -2 ---equation 1
3x - 2y - 2z= -3 ---equation 2
-5x + 3y + 4z=7 ---equation 3
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For this system, you can do Substitution method
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From equation 1
2x + y + z = -2
y = -2x - z - 2 ----equation 1'
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From equation 2
3x - 2y - 2z = -3
2y = 3x - 2z + 3
y = 1/2 (3x - 2z + 3) ----equation 2'
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Equate equations 1' and 2'
-2x - z - 2 = 1/2 (3x - 2z + 3)
Cross multiply 2
-4x - 2z - 4 = 3x - 2z + 3
-4x - 3x - 2z + 2z = 3 + 4
-7x = 7
x = -1
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From equation 3
-5x + 3y + 4z=7
3y = 5x - 4z + 7
y = 1/3[5x - 4z + 7] ----equation 3'
Substitute x=-1
y = 1/3[5(-1) - 4z + 7]
y = 1/3 [-5 - 4z + 7]
y = 1/3 [-4z + 2] ----equation 4
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From equations 1'
y = -2x - z - 2 (x=-1)
y = -2(-1) - z - 2
y = 2 - z - 2
y = - z -------equation 5
Equate equation 5 to 4
-z = 1/3 [-4z + 2]
-3z = -4z + 2
-3z + 4z = 2
z = 2
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Substitute z=2 to equation 5
y = -z
y = -2