Question

The following system of equations lacks solutions when b ≠ - c

Answer 1

Answer:

These lines have the same slope and will never intersect unless the y offset is identical.  This will only happen when b is equal to -c.

Step-by-step explanation:

Let's reformat these to match, starting with the first one:

$2ax - y + b = 0\\-y = -2ax - b\\y = 2ax + b$

And the second one:

$2y - 4ax+2c = 0\\2y = 4ax - 2c\\y = 2ax - c$

It now shows clearly that these are both lines with same slope and differ only by the y position, depending on the values of b and c.  If b is equal to negative c, then both lines are identical, otherwise they are parallel and never intersect.