Question 137979This question is from textbook
: How do you solve this system?
x + 2y-3z = -8
2x + y + 3z= 17
x - 3y + 3z = 11 This question is from textbook
You can put this solution on YOUR website! How do you solve this system?
x + 2y-3z = -8
2x + y + 3z= 17
x - 3y + 3z = 11
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You could solve it Gauss-Jordan elimination or with Cramer's Method.
I used the Matrix method on a TI calculator to get:
x = 2
y = 1
z = 4
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Cheers,
Stan H.
x + 2y-3z = -8 //First Equation
2x + y + 3z= 17 //Second Equation
x - 3y + 3z = 11 //Third Equation
Lets add the first and second equations to remove "z"
x + 2y - 3z = -8
+ 2x + y + 3z = 17
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3x + 3y = 9 //This will be our 4th equation
Lets add the first and third equations to remove "z"
x + 2y - 3z = -8
+ x - 3y + 3z = 11
---------------------
2x - y = 3 //This will be our 5th equation
Reform the 4th equation
3x + 3y = 9
3x = 9 - 3y
x = (9 - 3y)(1/3)
x = 3 - y
Now substitute this x value to the 5th equation
2(3 - y) - y = 3
6 - 2y - y = 3
6 - 3y = 3
-3y = 3 - 6
-3y = -3
y = 1 //Value for "y"
Substitute this value of "y" to 4th equation
3x + 3(1) = 9
3x + 3 = 9
3x = 9 - 3
3x = 6
x = 2
Now we have the values for "x" and "y"
Substitute this values of "x" and "y" to first equation
(Actually you can substitute this to any of the first 3 equations)
(2) + 2(1) - 3z = -8
2 + 2 - 3z = -8
4 - 3z = -8
-3z = -8 - 4
-3z = -12
z = 4
To check your answer substitute and x-y-z values any of the first three equations (If you use the 1st equation to solve for z then you must not use it for checking. Same thing for the 2nd and the 3rd equations)
I'll substitute to the 3rd equation
(2) - 3(1) + 3(4) = 11
2 - 3 + 12 = 11
-1 + 12 = 11
11 = 11
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