I have system of equation contain of two equations

**eq1:=a1*x^2+b1*y^2+c1*x*y+d1*x+e1*y+f1:**

**eq2:=a2*x^2+b2*y^2+c2*x*y+d2*x+e2*y+f2: **

I want to find the number **k **so that the equation

**a1*x^2+b1*y^2+c1*x*y+d1*x+e1*y+f1 + k*(a2*x^2+b2*y^2+c2*x*y+d2*x+e2*y+f2) = 0**

can be factor, where** k **satisfy

**a:=a1+k*a2:**

**b:=b1+k*b2:**

**c:=c1+k*c2:**

**d:=d1+k*d2:**

**e:=e1+k*e2:**

**f:=f1+k*f2:**

I tried

**A:=a*x^2+b*y^2+c*x*y+d*x+e*y+f: **

**collect(A,x);**

**B:=collect(discrim(A, x), y); **

**C:= discrim(B,y);**

and got the expression

**-16*(4*a*b*f-a*e^2-b*d^2-c^2*f+c*d*e)*a=0.**

For example** **

> **restart:**

**a1:=14:**

**b1:=-21:**

**c1:=0:**

**d1:=-6:**

**e1:=45:**

**f1:=-14:**

**a2:=35:**

**b2:=28:**

**c2:=0:**

**d2:=41:**

**e2:=-122:**

**f2:=56:**

**a:=a1+k*a2:**

**b:=b1+k*b2:**

**c:=c1+k*c2:**

**d:=d1+k*d2:**

**e:=e1+k*e2:**

**f:=f1+k*f2:**

**P:=c*d*e+4*a*b*f-a*e^2-b*d^2**

**-f*c^2:**

**eq1:=a1*x^2+b1*y^2+c1*x*y+d1*x+e1*y+f1:**

**eq2:=a2*x^2+b2*y^2+c2*x*y+d2*x+e2*y+f2:**

**with(RealDomain):**

**Q:=solve(P=0,k);**

**factor(eq1+Q*(eq2));**

**solve([**

**eq1=0,eq2],[x,y]);**

Where**, Q **is** k** which I want to find.** **

My question is, if I have the system of equations

**eq1:=a1*x^3+b1*y^3+c1*x^2*y+ d1*x*y^2 + e1*x+f1*y+g1:**

**eq2:=a2*****x^3+b2*y^3+c2*x^2*y+ d2*x*y^2 + e2*x+f2*y+g2**:

How can I get a similar to the

**-16*(4*a*b*f-a*e^2-b*d^2-c^2*f+c*d*e)*a=0?**

** **