Having an Issue with Solve with functions in the equations

Questions
1

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:=-7+a x+y and g2:=-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?

2

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

3

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))}}
4 
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))}}

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