Having an Issue with Solve with functions in the equations

GROUPS:
 The online instructions for Solve give the following example of solving 2 linear equations:Solve[-7 + a x + y == 0 && -1 + b x - y == 0, {x, y}]Giving the following output::{{x -> 8/(a + b), y -> -((a - 7 b)/(a + b))}}However, if I define two functions g1 and g2 like this:g1[x_]:=-7+a x+y   and g2[x_]:=-1+b x-y    (these are the left sides of the two equations in the above example),and then if I write:  Solve[g1==0, g2==0, {x,y}]I get the following:Solve::ivar: -1+b x-y==0 is not a valid variable. >>Solve[-7 + a x + y == 0, -1 + b x - y == 0, {x, y}]Why can't I put a function like g1 or g2 into Solve?
Answer
4 years ago
3 Replies
 The above listing is my first attempt on this forum, so I'm not up to speed on the details of how to enter something. But i see that although I typed in the line Solve[g1==0,g2 somehow the got left off immediately after g1 and g2. It probably will do it again here. So please note that what I actually typed has the open square bracket, x, close  square bracket  after g1 and g2 in my Solve expression that does not work.Ken Bures
Answer
4 years ago
 Ilian Gachevski 1 Vote According to the error message, -1 + b x - y == 0 appears in the place where Solve expected the variable(s). Try something like In[1]:= g1[x_, y_] := -7 + a x + y; g2[x_, y_] := -1 + b x - y;  In[2]:= Solve[{g1[x, y] == 0, g2[x, y] == 0}, {x, y}]  Out[2]= {{x -> 8/(a + b), y -> -((a - 7 b)/(a + b))}}  In[3]:= Solve[g1[x, y] == 0 && g2[x, y] == 0, {x, y}]  Out[3]= {{x -> 8/(a + b), y -> -((a - 7 b)/(a + b))}}
Answer
4 years ago
 In[1]:= Solve[-7 + a x + y == 0 && -1 + b x - y == 0, {x, y}]  Out[1]= {{x -> 8/(a + b), y -> -((a - 7 b)/(a + b))}}  In[2]:= g1[x_, y_] := -7 + a x + y;         g2[x_, y_] := -1 + b x - y;         Solve[g1[x, y] == 0 && g2[x, y] == 0, {x, y}]  Out[4]= {{x -> 8/(a + b), y -> -((a - 7 b)/(a + b))}}Note: I make heavy use of the little <> icon towards the right end of the second row above the reply box. That used to provide a single box where code could be pasted and would usually not be corrupted in the process. Now it makes multiple single line boxes when I paste code, but I scrape-n-paste-delete-empty-boxes to accomplish the same. And I check carefully both before and after clicking the Publish button, and repeatedly edit if need be, to get the posting to be something that can be directly scrape-n-pasted into a notebook by the readers.
Answer
4 years ago