Question

How do you determine whether a linear system has one solution, many solutions, or no solution when given 11x = 2y - 1 and 3y = 10 + 8x?

Answer 1

This equation has one root.

Explanation:

In order to determine how many root a equation like this has, you must know at how many points do they intersect. Both are equation of straight lines so most probably the intersect at one point or do not intersect at all.
Firstly you solve for value of x.
11x=2y-1
2y=11x+1
y=`(11x+1)/2`
Now replace this value of y in another equation,

you will get value of x as 1.

Now here you see, since there is only one value of x where the two lines meet each other, so the root is one.
If you receive no value of x means that these lines are probably parallel and they do not meet.
In this case it has only one solution.