1)  Make up a system of equations that does not have a solution. 
Describe how you determined the equations.


2)  Make up a system of equations that has infinitely many solutions. 
Describe how you determined the equations.


3)  Think about a graph of a line (or system of lines) in a real world
case.  What does the slope represent in your graph?  What does the
y-intercept represent?  What does the x-intercept represent?

Hello and thank you for your question.

1.  If you'll picture two parallel lines, you'll realize that since
they don't intersect there can't be any point that's common to both of
them, so there's no solution.  What makes them parallel is that they
have the same slope.

So using the general formula
y = mx + b  [where m is the slope and b is the y-intercept]
if we give them the same 'm' and different b's we'll have it.

y = 3x + 1
y = 3x + 2

2.  For infinite solutions, you'll want two lines that are really the
same line.  They intersect everywhere so they have infinite solutions.
 You can get this by multiplying each term in the first equation by
the same number.

 y = 3x + 1
2y = 6x + 2

3.  Let's use the formula that converts Celsius temperature to Fahrenheit.
    We'll use Y for the Fahrenheit and X for the Celsius temperature.
Y = 1.8X + 32

So for example a Celsius temperature of 100 is the same as a
Fahrenheit temperature of 212.

The slope of the graph is 1.8   
It represents the size ratio of Celsius and Fahrenheit degrees (each
Celsius degree is 1.8 times bigger a Fahrenheit degree).

The Y-intercept (when X is zero) is 32.  It represents the Fahrenheit
temperature corresponding to zero Celsius.

The X-intercept (when Y is zero) is
X = -32 / 1.8
X = -17.78
It represents the Celsius temperature corresponding to zero Fahrenheit.

No Google search for this - - I knew it
[I did use Google to do the division]
://www.google.com/search?hl=en&lr=&ie=UTF-8&q=32%2F1.8

Thanks again for letting us help.  If you find any of this unclear,
please request clarification.  I would appreciate it if you would hold
off on rating my answer until I have a chance to respond.

Google Answers Researcher
Richard-ga

This is my first Google Answer experence and I am very impressed. This
was done in a very timely manner and very helpful.