The following system of equations lacks solutions when b ≠ - c Show that it is so or explain why it is so.

2ax - y + b = 0
2y −4ax + 2c = 0

Show that it is so or explain why it is so.

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:

And the second one:

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.

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step-by-step explanation:

the mistake in the pattern is that :

b. the decimal point was moved one too many place values each time

the correct pattern could be made by :

b. moving the decimal point to the right the same numbers of place values as the exponents