what does no solution mean in math

Question

anonymous · Answer

depends on the context

jamesj · Answer

For example: "What is the integer n such that 2n = 1?"

That problem has no solution.  I.e., there is no integer n such that 2n = 1.

anonymous · Answer

for example 
$$x+3=x+5$$ has no solution 
$$\frac{3}{5-5}$$ has no solution and what jamesj said has no solution.

anonymous · Answer

also "find the intersection of 
$$x-y=5$$ and 
$$2x-2y=4$$ 
has no solution. so it really depends on the context of the question i think

anonymous · Answer

like these 
a. 3x + 1 = 2x + 1
b. 3x + 1 = 3x + 1
c. 3x + 1 = 3x + 2

anonymous · Answer

ok for the first one solve 
$$3x+1=2x+1$$
$$x+1=1$$
$$x=0$$ is a solution

anonymous · Answer

second one 
$$3x+1=3x+1$$ is an identity, true for all values of x

anonymous · Answer

third one 
$$3x+1=3x+2$$ as no solution because if you tried to solve it by say subtracting 3x from both sides you would get 
$$1=2$$ which is false

anonymous · Answer

so the answer is 3x+1=3x+2 is the one that has no soulution ?

anonymous · Answer

yes, that is the one with no solution.

anonymous · Answer

thank you