Question

Find the value of K for which the following pair of linear equations have infinitely many solutions: 2x + 3y = 7, (k + 1)x + (2k - 1)y = 4k + 1 Option 1: K = 3 Option 2: K = -1 Option 3: K = 1 Option 4: K = 2

Answer 1

Option 4: K = 2. The value of K that yields infinitely many solutions for the given pair of linear equations is K = 2. This is determined by setting up equations for the ratios of the coefficients and the constants and finding the option that satisfies both equations.

Step-by-step explanation:

In this math problem, the pair of linear equations will have infinitely many solutions if, and only if, the ratios of the coefficients of x and y are equal to the ratios of the constants. Therefore, we set up the following equations for the coefficients and the constants using the given linear equations:

2 / (k + 1) = 3 / (2k - 1) and 7 / (4k + 1) = 2 / (k + 1)

By substituting the given options into these equalities, you find that the only solution that satisfies both equalities is when K = 2.

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