The normal vector to the plane (E) (assumedly) is n=(2,1,1), being the coefficients of the equation. If vector r=(x,y,z) for any point on the plane and r1=(a,b,c) is the vector for P, then n•(r-r1)=0=n•r-n•r1=1-(2a+b+c)=0, from which a=(1/2)(1-b-c). The same result is obtained by simply plugging (a,b,c) into the equation of the plane. Therefore 7a+b+c=(7/2)(1-b-c)=7/2-7(b-c)/2+b+c=7/2-5(b-c)/2.
E has not been defined so we cannot relate P to anything except the given plane.