Final answer:
The constants k and p for the provided solution (-2, p) in the simultaneous equations are -7 and 15 respectively. The pair (-2, 15) is the only solution for the given simultaneous equations.
Step-by-step explanation:
First, let's plug in the provided solution (-2, p) to the simultaneous equations to find the values of k and p. So we have -2 - 5 = k and 3^2 = p - 6. Simplifying these equations, we get -7 = k and 9 = p - 6, which implies k = -7 and p = 9 + 6 = 15.
Second, to find the other pair of solutions, note that for any pair of solutions to be valid, they must satisfy both equations given. This means if we plug the solutions into both the equations they should hold true. Suppose we have another pair of solutions (n, m), it must satisfy n - 5 = -7 and 3^2 = m - 6. Solving these equations, we obtain n = -7 + 5 = -2 and m = 9 + 6 = 15 which are exactly the values for x and y we had before. This means the pair (-2, 15) is the only one pair of solutions for the given simultaneous equations.
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