Find the value of `k` for which the following system of linear equations has infinite solutions: `x+(k+1)y=5,\ \ \ \ (k+1)x+9y=8k-1`

Explanation

To find the value of \( k \) for which the given system of linear equations has infinite solutions, we need to use the condition for infinite solutions. The equations are:

1. \( x + (k + 1)y = 5 \) (Equation 1)
2. \( (k + 1)x + 9y = 8k - 1 \) (Equation 2)

### Step 1: Identify coefficients
From the equations, we can identify the coefficients:
- For Equation 1:
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