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Question 41176: use the Gauss-Jordan elimination to solve the following system of equations.
x+y+z=2
2x-3y+z=-11
-x+2y-z=8
Answer by zeynep(43)   (Show Source):
You can put this solution on YOUR website! x+y+z=2
2x-3y+z=-11
-x+2y-z=8
Let's add the first and the third equations. Since x's and z's in these equations have opposite coefficients, we can drop them out.
x+y+z=2
-x+2y-z=8
3y=10 (divide each side by 3)
3y/3=10/3
y=10/3
Let's plug in the value of y in the first equation.
10/3+y+z=2 (move 10/3 to the right of the equation)
x+z=2-10/3
x+z=-4/3
Now, let's plug the value of y in the second equation.
2x-3y+z=-11
2x-3.(10/3)+z=-11
2x-10+z=-11 (move -10 to the right of the equation)
2x+z=-11+10
2x+z=-1
Now we have found;
x+z=-4/3
2x+z=-1
Let's multiply the first equation by -1 to create opposite coefficients for z.
-x-z=4/3
2x+z=-1
Now let's add the two equations to drop out z;
x=1/3
When we plug the value of x in the first equation (you may plug it in the second equation as well);
-1/3-z=4/3 (move -1/3 to the right of the equation)
-z=4/3+1/3
-z=5/3 (divide each side by -1)
z=-5/3
So, y=10/3, x=1/3, z= -5/3
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