There are 23 students in a karate class. the number of girls is less than twice the number of boys. write two systems of equations.

Let's call the girls "x" and the boys "y".

first equation is this one:
There are 23 students in a karate class.

this we would write:
x+y=23

and the second equation can be found from this sentence:

The number of girls is less than twice the number of boys

which means:
x<2y.

Now, that's an inequality, but it's all we can do here, since the question doesn't tell us anything more - also, we can's solve it exactly.

we could say, for example that it's less by 1, then it would be:
x-1=2y.

but the question doesn't say by how much less!