Finding a third equation for a unique solution to a 3×3 system

[Naeem]

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]

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 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.

 

[HallsofIvy]

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).