its been 2 years and i cant remember where to begin

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haley

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Jan 29, 2006
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okay this is my first time taking a math class in 2 years and i got put into a math 105 course and i cant even remember where to begin! :oops:
x-y+2z=-3
x+2y+3z=4
2x+y+z=-3

i remember you have to solve for each variable but i cant even remember how to start
 
What method(s) did they cover in class for solving linear systems? Or are you asking for lessons so you can learn a method or two?

Thank you.

Eliz.
 
just learning the methods themselves please i dont even know where to begin with them
 
haley said:
okay this is my first time taking a math class in 2 years and i got put into a math 105 course and i cant even remember where to begin! :oops:
x-y+2z=-3
x+2y+3z=4
2x+y+z=-3

i remember you have to solve for each variable but i cant even remember how to start
Click to expand...

Here's how I would start. I'd see if I could turn this system of three equations in three variables into a system of two equations in two variables.

Let me number the equations for easier reference:
1) x - y + 2z = -3
2) x + 2y + 3z = 4
3) 2x + y + z = -3

Add equations 1) and 3):
1) x - y + 2z = -3
3) 2x + y + z = -3
----------------------
4) 3x + 3z = -6

Hmmm.....we could divide both sides of this equation by 3 to produce a "new and improved" version of equation 4):
4) x + z = -2

Next, let's multiply both sides of equation 1) by 2:
1) 2x - 2y + 4z = -6

Add this to equation 2:
1) 2x - 2y + 4z = -6
2) x + 2y + 3z = 4
-------------------
5) 3x + 7z = -2

Now we have two equations in two variables:
4) x + z = -2
5) 3x + 7z = -2

Hopefully you can still remember how to solve a system of two equations in two variables.....
 
Lets try one method of elimation and sub.

x-y+2z=-3 called eqn(1)
x+2y+3z=4 called eqn (2)
2x+y+z=-3 called eqn (3)

now the aim is to "modify" each equation so when any 2 equations are added or subtracted then one variable cancels out.

Take equation (1) and subtract equation (2) from it

x-y +2z -(x+2y+3z) = -3 - 4
-3y - z = -7 call this equation (4)

Next take equation (3) and subtract 2 times equation (2)...

equation (2) times 2 ...
2x + 4y +6z = 8 call this equation (2a)

equation (3) minus equation (2a)

-3y -5z = -11 called equatio (5)

Now focus on equation (4) and (5)

-3y - z = -7 call this equation (4)
-3y -5z = -11 called equatio (5)

Take equation (4) minus equation (5)

4z = 4
z = 1

Now place this value back into equation (4) or (5) and find what y is.
Repeat this with equation (1),(2) or (3) to find x.

Questions......
 
Haley, just to remind you there are lots of plans of attack: :wink:

x - y + 2z = -3 [1]
x + 2y + 3z = 4 [2]
2x + y + z = -3 [3]

Add [1] + [3]:
3x + 3z = -6
-3x = 3z + 6 [4]

double [1]:
2x - 2y + 4z = -6
x + 2y + 3z = 4 [2]
add 'em:
3x + 7z = -2
-3x = 7z + 2 [5]

from [4] and [5]:
7z + 2 = 3z + 6
4z = 4
z = 1
 
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