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.