Question

Given that the value of b can never be equal to -1, how do you determine if the equations are intersecting, parallel, or coincident: `x+y=ab, bx-y=a`?

Answer 1

Check whether the Determinant is non-zero.

Explanation:

If the equations do not intersect into a unique equation, the Determinant will be zero.

From the reference, the determinate of the two equations is:

#| (1, 1), (b, -1) | = -1 - b#

The only what this can be zero is, if `b = -1`, and we are given that this is not allowed, therefore, the equations have a unique solution.