Need help with this have exam tommorow. (1 Viewer)

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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,
 

LeonhardEuler

Gold Member
858
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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,
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 eqautions. 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.
 

HallsofIvy

Science Advisor
41,626
821
Or: solve the two equations for x, y in terms of z. Choose whatever value for z you want, calculate x,y for that z and just make up a linear equation that they will solve (for example x+ y+ z= whatever their actual sum is).
 

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