Answer:
x=-30/71, y=0
Step-by-step explanation:
if a vector satisfies an equation of the form ax+by+cz=0 then the vector is
parallel to the plane ax+by+cz=0, and, the cross product of two vectors results in an orthogonal vector to both.
So, <a,b,c> the normal vector of the plane ax+by+cz=0, can be found as the cross product of the two parallel vetors to the plane:
<a,b,c> = <6,-5,-5>×<7,4,6>= <-10,-71,59>
so, the homogeneous system is:
-10x-71y+59z=0
by replacing the vector <3,x,y> in the system
-30-71x+59y=0
So, there are 2 unknown variables and 1 equation, it means that 1 variable is free
so, y=0 is a random defition and x can be obtain with the equation
-30-71x=0 -> x=-30/71
