Final answer:
The values of variables x and y that equate the two matrices are 3 and -4 respectively, and the constant k is -1. These solutions are checked and confirmed reasonable.
Step-by-step explanation:
The question is about comparing two matrices and finding the values of variables x and y, and the constant k that make the matrices equal. We can determine the values by setting the corresponding elements of the matrices equal to each other.
From the given matrices [[x+3, y+4], [7, -1]] = [[6, 0], [7, k]], we compare the elements:
- x + 3 = 6
- y + 4 = 0
- 7 = 7
- -1 = k
By solving the equations above, we get:
- x = 6 - 3 = 3
- y = 0 - 4 = -4
- k = -1
After finding the values for x, y, and k, it's important to check if the solutions are reasonable. In this case, we can confirm that the solutions make sense because when we plug them back into the original matrix, we get the same matrix as the one we are comparing it to.