Part B : Multiple Solutions.

When I see an equation system like this one

ABC = 4

3A + 2B - C = 3 ,

I think Graphing software is the best to start with.

Because there is more then one solution since there are 2 equation for 3 variables and first one is not that easy to solve.

So I entered these values to Graphing Calculator and it constructed this shape

Click HERE for GCF file.

So there are four regions on 3-dimensional space that ABC=4 can be drawn

These are (A>0,B>0,C>0) , (A>0,B<0,C<0) , (A<0,B<0,C>0) and (A<0, B>0,C<0)

3A + 2B - C = 3 is a plane and this plane intersects three of the four regions.

It doesn't intersect (A<0,B<0,C>0).

I want t o change equation system to 2 variables system.

ABC = 4

3A + 2B - C = 3  

then  3A + 2B - 3 = C , plugging this equation on the first one gives.

so A.B.( 3A + 2B - 3)=4

Graph of this equation is

From here we can estimate A (x-axis) and B (y-axis) then we can put it these values in 3A + 2B - 3 = C  so we can find C

This equation can be explored in graphing calculator.