Answer:
The system of linear equations has infinitely many solutions
Step-by-step explanation:
Let's modified the equations and find the answer.
Using the first equation:
 we can multiply by 2 in both sides, obtaining:
 we can multiply by 2 in both sides, obtaining:
 which can by simplified as:
 which can by simplified as:
 which is equal to:
 which is equal to:

Considering the second equation:

Taking into account that from the first equation we know that:  , we can express the second equation as:
, we can express the second equation as:
 , which can be simplified as:
, which can be simplified as:
 


Because (-8) is being divided by (2+k), then (2+k) can't be equal to 0, so:
 if
 if 
This means that k can be any number different than -2, and for each of these solutions, there is a different solution for y, allowing also, different solutions for x.
For example, if k=0 then 
 which give us y=-4, and, because:
 which give us y=-4, and, because:
 if y=-4 then
 if y=-4 then 
Now let's try with k=-1, then:
 which give us y=-8, and, because:
 which give us y=-8, and, because:
 if y=-8 then
 if y=-8 then  .
.
Then, the system of linear equations has infinitely many solutions