Given the system of equations in two variables a1*x + b1*y = c1, a2*x + b2*y = c2, assign possible values of a1, b1, c1, a2, b2, c2 to make the system consistent and independent.

 

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The system of equations a1*x + b1*y = c1 and a2*x + b2*y = c2 has to be made consistent and independent.

A system of equations is consistent and independent if the graph of the two lines a1*x + b1*y = c1 and a2*x + b2*y = c2 intersects only at one point.

For this the coefficients of the terms of any equation should not have a common factor that can be canceled to yield the other equation. Also, a1/b1 `!=` a2/b2 to ensure that the lines are not parallel.

The values of a1, b1, c1, a2, b2, c2 should be such that we get two separate lines that intersect only at one point.

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