### Taking elements in solve and multiplying to a polynomial

So I want a function that solves a system of two equations and the move those numerical results to polynomials f and g.

~~ ~~def PolynomialCoefficient(fcn1, fcn2):
var ('a b')
~~eqn1= 2*a+2*b==0
eqn2= 3*a-b==1
List=solve([eqn1,eqn2],a,b)
~~ eqn1 = 2*a + 2*b == 0
eqn2 = 3*a - b == 1
List = solve([eqn1, eqn2], a, b)

Now I want to move this to ~~a~~*f(x)+b*g(x) `a*f(x)+b*g(x)`

without hitting solve each ~~time ~~time
and manually typing what ~~a and b ~~`a`

and `b`

are. For ~~example, PolynomialCoefficient(x,y) ~~example,
`PolynomialCoefficient(x, y)`

should output

`1/4 x - `~~1/4y. ~~1/4 y

. The issue ~~is ~~is

```
len(List)
```

outputs 1. If it was length 2 with ~~a ~~`a`

in first slot and ~~b ~~`b`

in 2nd ~~slot ~~slot, I ~~can do, ~~could do

~~Poly= List[0]*fcn1+List[1]*fcn2
~~ Poly = List[0]*fcn1 + List[1]*fcn2
return Poly

Any ideas on how to move ~~a and b?~~`a`

and `b`

?