Which is equivalent to
14x-3y+2z=100
-17x+8y+10z=11
-3+13y+29z=81
x = -7717/335
y = -36738/335
z= 16662/335
To find the equivalent system of equations, we need to manipulate the given equations until we have coefficients of x, y, and z that are the same.
Let's start by multiplying the second equation by 2 to eliminate the fractions:
2 * (-17x + 8y + 10z) = 2 * 11
-34x + 16y + 20z = 22
Next, we'll multiply the third equation by 4 to eliminate the fractions:
4 * (-3 + 13y + 29z) = 4 * 81
-12 + 52y + 116z = 324
Now, we have the following system of equations:
14x - 3y + 2z = 100 (Equation 1)
-34x + 16y + 20z = 22 (Equation 2)
-12 + 52y + 116z = 324 (Equation 3)
To eliminate the variable x, let's multiply Equation 1 by 2 and add it to Equation 2:
2(14x - 3y + 2z) + (-34x + 16y + 20z) = 2 * 100 + 22
28x - 6y + 4z - 34x + 16y + 20z = 200 + 22
-6x + 10y + 24z = 222 (Equation 4)
To eliminate the variable x in Equation 3, let's multiply Equation 1 by 4 and subtract it from Equation 3:
4(14x - 3y + 2z) - (-12 + 52y + 116z) = 4 * 100 - 324
56x - 12y + 8z + 12 - 52y - 116z = 400 - 324
56x - 52y - 12y + 8z - 116z = 76
56x - 64y - 108z = 76 (Equation 5)
Now we have the following system of equations:
-6x + 10y + 24z = 222 (Equation 4)
56x - 64y - 108z = 76 (Equation 5)
These two equations are equivalent to the original system of equations you provided.
-3 ??? x ???? +13y+29z=81
and what do you want? A solution using Gauss Jordan ? If so go to:
http://www.gregthatcher.com/Mathematics/GaussJordan.aspx
14x-3y+2z=100
-17x+8y+10z=11
-3x+13y+29z=81