Explain this easily please

8.1 For all values of p, find the solutions of the system px+ y = x - y+z=0 2y - z = 3 SECTION 16.8 / CRAMER'S RULE 655 Solution: The coefficient matrix has determinant IA| = 1 -p 0 According to Theorem 16.8.1, the system has a unique solution if 1 -p # 0-that is, if p # 1. In this case, the determinants in (16.8.2) are DI O D2 = 10 and D3 : 1 0 13 10 3 2 31 whose numerical values are D, = 2, D2 = 1 - 3p, and D3 = -1 - 3p. Then, for p * 1, Eq. (16.8.4) yields DI 2 y= D2 1 - 3p D3 -1 - 3p x = IAl IAl and 1 - p Z= IAl 1 - P On the other hand, in case p = 1, the first equation becomes x + y = 1. Yet adding the last two of the original equations implies that x + y = 3. There is no solution to these two contradictory equations in case p = 1.9