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3x3 2014.notebook March 20, 2015
Homework SolutionsI can solve of system of linear equations
Solving 3 Equations for 3 Unknown Variables
I can solve of system of 3 equations
3x3 2014.notebook March 20, 2015
Consider a linear equation in 3 variables x, y, and z, such as 3x - 2y + z = 7. Any ordered triple (x, y, z) that makes the equation true is said to be a solution to the equation. For example, (2, 1, 3) is a solution. However, (5, 2, 4) is not a solution. There are infinitely many solutions in this solution set.
I can solve of system of 3 equations
The graph of a linear equation in 3 variables is a plane, not a line. There are various ways in which 3 planes can be related. Look at the images to the left to see some of the relationships.
I can solve of system of 3 equations
3x3 2014.notebook March 20, 2015
I can solve of system of 3 equations
Using 2 equations (eqs 1 & 2 OR eqs 1 & 3 OR eqs 2 & 3) and eliminate a variable. (Use additioneliminate)You will end up with a new equation (eq 4) that will still have two variable.
Repeat step 1 using 2 different equations and eliminate the SAME variable. For example if you used eqs 1 & 2 you could use eqs 1 & 3 or 2 & 3 at this point. This will be new equation (eq 5) that will also have the same variables as eq 4.
Using your 2 new equations (eqs 4 & 5) solve using additionelimination for one variables.
Now that you found one variable after completing step 3, substitute it back into either equation 4 or 5 and find the other variable.
Finally, using the two variables you now know substitute both back them into one of your original eqs 1, 2, or 3 to find the remaining variable.
Check (3 checks)
Steps for solving 3 equations/ 3 unknowns
Step 1.
Step 2.
Step 3.
Step 4.
Step 5.
Step 6.
Example #1 2x - y + z = 03x - 2y + 4z = 115x + y - 6z = -32( , , )
eq 1)
eq 2)
eq 3)
2x - y + z = 0 3x - 2y + 4z = 11
-2( 2x - y + z = 0) 3x - 2y + 4z = 11
eq 1)
eq 2)-4x + 2y - 2z = 0 3x - 2y + 4z = 11 - x + 2z = 11
Step 2.
Step 1.2x - y + z = 05x + y - 6z = -327x - 5z = -32
eq 1)
eq 3)
eq 4)
eq 5)
I can solve of system of 3 equations
3x3 2014.notebook March 20, 2015
Example #1 2x - y + z = 03x - 2y + 4z = 115x + y - 6z = -32( , , )
eq 1)
eq 2)
eq 3)
7x - 5z = -32 7x - 5z = -32 (7)( -x + 2z = 11) -7x +14z = 77
9z = 45 z = 5
Step 3.
7x - 5z = -32eq 4)
- x + 2z = 11eq 5)
I can solve of system of 3 equations
7x - 5z = -32eq 4)
- x + 2z = 11eq 5)
Step 4. z = 5- x + 2z = 11
- x + 2(5) = 11- x + 10 = 11 -x = 1x= - 1
eq 5)
Example #12x - y + z = 03x - 2y + 4z = 115x + y - 6z = -32( -1 , ? , 5 )
eq 1)
eq 2)
eq 3)
2x - y + z = 0 2(-1) - y + 5 = 0-2 -y + 5 = 0-y + 3 = 0-y = -3y = 3
Step 5. x= - 1, y = ? , z = 5eq 1)
I can solve of system of 3 equations
3x3 2014.notebook March 20, 2015
Example #1 2x - y + z = 03x - 2y + 4z = 115x + y - 6z = -32( -1 , 3 , 5 )
eq 1)
eq 2)
eq 3)
I can solve of system of 3 equations
Step 6. x= - 1, y = 3 , z = 5
2x-y+z = 02(-1)-3+5=0-2 - 3 + 5=0-5 + 5 = 00 = 0
eq 1) 3x-2y+4z=113(-1)-2(3)+4(5)=11-3-6+20=11-9+20=1111 = 11
eq 2) eq 3)5x+y-6z=-325(-1)+3-6(5)=-32-5+3-30=-32-2-30=-32-32=-32
Solve for all 3 variables:x + y + z = 4x - 2y -z = 12x - y - 2z = -1
I can solve of system of 3 equations
3x3 2014.notebook March 20, 2015
Solve for all 3 variables:x + y + z = 4x - 2y -z = 12x - y - 2z = -1
I can solve of system of 3 equations
Solve for all 3 variables:x + y + z = 4x - 2y -z = 12x - y - 2z = -1
I can solve of system of 3 equations
3x3 2014.notebook March 20, 2015
HomeworkI can solve a system of 3 equations
