The discussion focuses on finding a third equation to ensure a unique solution for the system of equations: 2x + 4y - z = 2 and x - y + 2z = 1. To achieve this, participants suggest that the new equation's coefficients must not be a linear combination of the existing equations' coefficients. A practical approach involves solving the two given equations for x and y in terms of z, then creating a linear equation based on the calculated values. This method guarantees a unique solution for the variables x, y, and z.
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Just FYI, this belongs in the homework section, but anyway: all's you need to do is find an equation such that the vector whose entries are the coefficents of the x, y and z variables is not a linear combination of the two vectors obtained from the other two equations. Pretty much all you need to do is make a guess and check that it works. To make life easy you should probably pick an easy equation like x=something.Naeem said:I have a system of equations
2x + 4y - z = 2
x - y + 2z = 1
I need to find a third equation so that there is a unique solution for the unknows x , y and z, and find them.
Please help
Thanks,