Final answer:
The value of k for which the pair of linear equations has infinitely many solutions is k = 16.
Step-by-step explanation:
In order for the pair of linear equations to have infinitely many solutions, the slopes and y-intercepts must be equal. Let's compare the given equations:
2x + ky = 8 -------- Equation (1)
kx + 8y=k -------- Equation (2)
In Equation (1), the slope is 2 and the y-intercept is 8/k. In Equation (2), the slope is k/8 and the y-intercept is k.
To have infinitely many solutions, the slopes and y-intercepts must be equal, so we can set up the following equations:
2 = k/8 -------- Equation (3)
8/k = k -------- Equation (4)
Solving Equation (3) for k, we get k = 16.
Substituting this value of k into Equation (4), we get 8/16 = 16. Thus, for k = 16, the pair of linear equations has infinitely many solutions.
Learn more about Solving Linear Equations