; Combine 3 quadratic polynomial equations with 3 unknown coefficients (a, b, c).
; Solve for variables (a), (b), and (c).

clear all ; restart Mathomatic
; enter all 3 equations:
y1=a+b*x1+c*x1^2
y2=a+b*x2+c*x2^2
y3=a+b*x3+c*x3^2
2 ; select equation number 2 as the current equation
eliminate a ; eliminate variable (a) from the current equation
3 ; select equation number 3
eliminate a b ; eliminate variables (a) and then (b) from the current equation
c ; solve and find (c)
simplify
2 ; select equation number 2 again
eliminate c using 3 ; find (b) by combining equation numbers 2 and 3
simplify
1 ; select equation number 1
eliminate c using 3 b using 2 ; find (a)

simplify fraction all ; list all solutions, converting to simple fractions