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Given a,b,c are integers, to show that the system have unique solution we have to find the value of the following determinant:
The value of this determinant is:
Since, this determinant is non-zero, by Cramer's rule the given system of equations have a unique solution.
Hence, x=0, y=0 and z=0 since each of the determinants `D_x` , `D_y` ,`D_z ` will contain a column of zeros (i.e the constant terms of the three equations).
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