Grade 11 Pre-Cal E

system of 3 linear equations

* 3 variables mean 3 equations

When given 3 linear equations:

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

Step 1: You should number your equations

Example:
1) x+y-z=2
2) x-2y+z=-1
3) 3x+y-2z=4

Step 2: Take two of the three equations and try to eliminate one of the three variables.

Example:
1) x+y-z=2
2) x-2y+z=-1
+_________
4) 2x-y = 1
Once you've eliminated one of the three variables, the new equation will become equation 4

Step 3: Now take the equation that you did not use in Step 2, and take one equation that you have used in Step2, then eliminate the same variable as in Step 2.

Example:
1)( x+y-z=2 ) 2 -----
3) 3x+y-2z= 4

2x+2y-2z = 4 <---
3x+y-2z=4
-_________ 5)
-x +y = 0
Once you've eliminated the same variables that you did in step 2, the new equation will become equation 5

Step 4: Now that you have equations four and five you can either subtsitute or eliminate one of the two remaning variables to sove for the other variable. Example: I will be using the subsitute method 4) 2x-y = 1 5) -x + y = 0 ----> y = x

2x-y = 1
2x- x = 1
x = 1 <--- solved variable

y = x
y = 1 <--- solved variable

Step 5 : now that you have solved two of the three variables you can now substitute the variables into one of the original equation to solve for the last variable.

Example:
x= 1
y = 1
1) x+y-z=2

1+1-z=2
2- z = 2
- z = 0
z = 0 <--- solved variable

(x , y , z)
(1 , 1 , 0)

You now have solved a three variable equation you should give your self a pat on the back.

The next scribe will be Eric.... oh wait he is not in this class SO the next scribe will be Francis ohh know he cant be he already scribed this month. the next scribe will be Rojuane

posted by RichardG @ 4:25 PM