Is this an example of infinite solutions?

[NiladriMathGeek]

The above is similar to the following equations
x + 0.y + 0.z = a
0.x + y + 0.z = b
0.x + 0.y + 0.z = 0

Is this an example of infinite solutions?

 

[Deleted member 4993]

View attachment 15238

The above is similar to the following equations
x + 0.y + 0.z = a
0.x + y + 0.z = b
0.x + 0.y + 0.z = 0

Is this an example of infinite solutions?

Yes ... z can be assigned any value.

But be careful. In the given set of equation - 'z' is an 'unnecessary' variable. By introducing this type of variable, any set of equations can be "rendered" artificially to have infinite solutions. No practical (physical) situation can give rise to these equations. These are 'pathological' examples.

 

[Steven G]

Befi

View attachment 15238

The above is similar to the following equations
x + 0.y + 0.z = a
0.x + y + 0.z = b
0.x + 0.y + 0.z = 0

Is this an example of infinite solutions?

Before I answer this I would like to know the meaning of all of the variables, especially z. To be honest I have never a seen a problem like this. The 3 equations you listed, were they the original eqs or have they been reduced? That would be nice to know!