# If there are an infinite number of solution to the system, what are the values of h and k in the following system? {(5x-9y=h),(8x+ky=-3):}

You need to consider the next two conditions for the system to have an infinite number of solutions, such that:

`Delta = [(5,-9),(8,k)] = 0`  (`Delta` represents determinant of matrix of coefficients of variables x and y)

`Delta =5k - (-9*8) => {(Delta = 5k + 72),(Delta = 0):} =>...

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You need to consider the next two conditions for the system to have an infinite number of solutions, such that:

`Delta = [(5,-9),(8,k)] = 0`  (`Delta` represents determinant of matrix of coefficients of variables x and y)

`Delta =5k - (-9*8) => {(Delta = 5k + 72),(Delta = 0):} => 5k + 72 = 0 => 5k = -72 => k = -72/5`

`Delta_1 = [(5,h),(8,-3)] ` = 0 (`Delta_1` represents characteristic determinant)

`Delta_1 = -15 - 8h => Delta_1 = {(Delta_1 = -15 - 8h),(Delta_1 = 0):} => -15 - 8h = 0 => 8h = -15 => h = -15/8`

Hence, evaluating k and h for the system to have an infinite number of solutions yields `k = -72/5` and ` h = -15/8.`

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