# Given the system of equations in two variables a_1 x+b_1 y=c_1 and a_2 x+b_2 y=c_2...   assign possible values of a_1, b_1, c_1, a_2, b_2, c_2 to make the system inconsistent and independent You need to impose the following conditions for the system to be inconsistent and independent determinant of matrix formed from coefficients of variables such that:

`Delta = [[a_1,b_1],[a_2,b_2]] = 0`

`Delta = [[a_1,b_1],[a_2,b_2]] = a_1*b_2 - b_1*a_2`

`a_1*b_2 - b_1*a_2 = 0 =gt a_1*b_2 =b_1*a_2 =gt a_1/a_2 = b_1/b_2`

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You need to impose the following conditions for the system to be inconsistent and independent determinant of matrix formed from coefficients of variables such that:

`Delta = [[a_1,b_1],[a_2,b_2]] = 0`

`Delta = [[a_1,b_1],[a_2,b_2]] = a_1*b_2 - b_1*a_2`

`a_1*b_2 - b_1*a_2 = 0 =gt a_1*b_2 =b_1*a_2 =gt a_1/a_2 = b_1/b_2`

You also need to impose the condition for caracteristic determinant of system such that:

`C = [[a_1,c_1],[a_2,c_2]] != 0`

`a_1/a_2 != c_1/c_2`

Hence, evaluating the relations between coefficients `a_1,a_2,b_1,b_2,c_1,c_2`  for the system to be inconsistent and independent yields `a_1/a_2 = b_1/b_2 != c_1/c_2` .

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