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...

## See

This Answer NowStart your **48-hour free trial** to unlock this answer and thousands more. Enjoy eNotes ad-free and cancel anytime.

Already a member? Log in here.

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.**