We want to solve the equations

A = 1.0 P + 0.1 V
B = 0.2 P + 1.0 V

for P. Multiplying the first equation by 10 we get

10 A = 10.0 P + 1.0 V
   B =  0.2 P + 1.0 V

and subtracting

10 A - B = 9.8 P 

so

P = (1/9.8) (10 A - B)