An equation is a sentence that uses an equals sign: $\,=\,$
An inequality is a sentence that uses an inequality symbol:
The phrase in two variables means that two different variables are used to determine
if the sentence is true.
In other words, you'll be choosing values for two different variables, and substituting these into the sentence,
to decide if it is true or false.
Most sentences in two variables are easy to spot, because you can ‘see’ two different variables.
Here's a simple example, to introduce important concepts and terminology:
Ah hah!
So, the picture of all the points that makes the equation $\,x+y = 5\,$ true is a line! See where the line crosses the $\,y$axis? That's the point $\,(0,5)\,$: $\,0 + 5 = 5\,$ See where the line crosses the $\,x$axis? That's the point $\,(5,0)\,$: $\,5 + 0 = 5\,$ Find the (approximate) location of the solutions $\,(1,4)\,$ and $\,(1.5,6.5)\,$ on the line. You'll want to bookmark wolframalpha.com. When you're bored, just type in equations and inequalities (you can start with the ones mentioned on this page) and see what you get. 
Of course, you can only see part of the graph—it goes on forever in all directions. In this case, you're looking at all the points that are on or above the graph of $\,x + y = 5\,$. Also, be careful—they're not showing the $\,x$axis and the $\,y$axis in this view: the bottom line isn't isn't the $x\,$axis, and the left vertical line isn't the $y\,$axis. 
One tricky type of ‘sentence in two variables’ is where you don't actually see two different variables,
since one of them has a coefficient of $\,0\,$.
What does this mean, exactly?
Consider the equation $\,x = 5\,$.
It looks like there's only one variable, $\,x\,$.
Viewed as an equation in one variable, there's only one solution—
the number $\,5\,$.
In this case, the graph is very, very boring—a single dot, at location $\,5\,$, on a number line.
However, the sentence $\,x = 5\,$ can also be viewed as an equation in two variables:
$\,x + 0y = 5\,$.
We don't bother to write the $\,0y\,$, since it's just zero—but it changes the solution set completely.
Now, since it's an equation in two variables,
a solution is an ordered pair—a choice for $\,x\,$ and a choice for $\,y\,$—that make the equation true.
What you notice pretty quickly is that $\,x\,$ must be $\,5\,$, but $\,y\,$ can be anything:
Thus, the solutions are ordered pairs of the form $\,(5,y)\,$, for all real numbers $\,y\,$.
What does this graph look like?
To get to any of these points, you start at the origin and move $\,5\,$ units to the right.
Then, you can move up/down to your heart's content.
The graph is the vertical line that crosses the $\,x$axis at $\,5\,$.
Wolfram Alpha has a bit of trouble with this one. Give it a break—it's a bit hard to see invisible things. But, we can get a great approximation to the graph by being a bit clever. Cutandpaste the following into wolframalpha.com: x + 0.00000001y = 5, 10 <= y <= 10 Notice that we've put a number really close to $\,0\,$ in front of the $\,y\,$. We're also specifying that we only want to see points whose $\,y$values are between $\,10\,$ and $\,10\,$. (Leave off the last part and see if you can figure out what's happening!) By the way, wolframalpha.com can plot it easily with just one word's help: plot x = 5 Try it! 
So, what's a person to do when they see an equation like ‘$\,x = 5\,$’?
Treat it as an equation in one variable?
In two variables?
(In three variables!?)
Context, context, context.
If someone says ‘graph $\,x=5\,$’ in high school,
then they're probably treating it as an equation in two variables.
If there's any doubt, just ask for clarification.
CONCEPT QUESTIONS EXERCISE:
On this exercise, you will not key in your answer.However, you can check to see if your answer is correct. Sentences like ‘$\,x = 5\,$’ are to be treated as sentences in two variables. 
PROBLEM TYPES:
