6.

If you add two equations and the resulting sum is a statement that cannot be true, such as 4 = 9, then the system has

solution (s).

The system has NO solutions

Step-by-step explanation:

Incompatible System of Equations

It's a system of equations that has no solutions because the conditions are contradictory. Let's set this equation:

x+y+3=5

It's clear that

x+y=2

Now, let's multiply the first equation by - 1

-x-y-3=-5

It continues to be that

x+y=2

The sum of two unknowns cannot change because we multiply an equation by a number. Now let's modify the last equation

-x-y+3=5

This equation leads to

x+y=-2

a contradictory condition since x+y should remain equal to 2. This equation and the first one form a system with no solutions. Let's now add the very first equation and this last modified one, we get

6=10

This contradictory outcome results from managing a system that has NO solutions