For what value of p, is the system of equations : p3x+(p+1)3y=(p+2)3 px+(p+1)y=p+2 x+y=1 consistent?

[c] The given system of equations are: p3x+(p+1)3y=(p+2)3                  .... (1) px+(p+1)y=(p+2)                 .... (2) x+y=1                                 .... (3) This system is consistent, if values of x and y from first two equation satisfy the third equation. which ⇒∣∣∣∣∣p3p1(p+1)3(p+1)1(p+2)3(p+2)1∣∣∣∣∣=0 ⇒∣∣∣∣∣p3p1(p+1)3−p310(p+2)3−p320∣∣∣∣∣=0 ⇒2(p+1)3−2p3−(p+2)3+p3=0 ⇒2(p3+1+3p2+3p)−2p3−(p3+8+12p+6p2)+p3=0⇒2p3+2+6p2+6p−2p3−p3−8−12p                                     −6p2+p3=0 ⇒−6−6p=0⇒p=−1