It is often helpful to multiply each equation by a different number to
prepare an "ADDITION" which will eliminate one (or in this case both) of the 2 variables:
Multiply the top equation by
-3
and the bottom equation by 2: |
-12x -18y = -18
12x + 18y = 24 |
|
Add the terms in each column:
0x + 0y = 6
which is false for all values of "x" and "y".
Since it is not possible to deduce such a false statement from true
statements by correct logic, we conclude that the original system cannot
be true for any choices of "x" and "y". This system is called
INCONSISTENT.
The solution: { } = empty set = Ø