SOLUTION: Graph the system of inequalities: y>or=x x<3

Question 206915: Graph the system of inequalities:
y>or=x
x<3

Answer by dlam5(15) (Show Source): You can put this solution on YOUR website!

There is the graph. But let's solve this LOGICALLY.
What I usually do is I forget about the inequality notations/signs, and say to myself: "what would this graph look like NORMALLY, when x=3, or y=x?"
Well, then I know for a fact that y=x just comes down on the graph SLANTED. Well, what does that mean? WHERE does it slant?
Plug in values for x and y to find out.
if...
x=1, y=1
The ordered pair (1,1) comes out.
if...
x=-5, then y=-5
The ordered pair (-5,-5) comes out.
I usually pick up to 5 VALUES of ordered pairs, then just play connect the dots. Now I know where it slants! (see graph)

Let's try x<3. Well, what does it look like if x = 3? I now find out 3 is a CONSTANT, so when graphed, I go right (because, 3 is positive) 3 on the x axis, and get a straight line, vertical..
Because, x = 3, x IS 3, so 3 right is a vertical line!
As I add the inequalities in, this tells me where the ordered pairs are okay to be (viable).
Well, how do I know where to shade? Pick a point not on the line for each equation.
y>or=x;
I'll pick 9,2 for example. This point (9,2) is NOT on the line.
9 is x; 2 is y.
is 2>or=9; NO! So, if 9,2 is close to the RIGHT of the graph, I SHADE opposite. Because all of that AREA isn't true. I shade to the left, as depicted on the graph.
Now, x<3. This is an easy one. It is saying "the x-values (x's) are LESS THAN (smaller) 3, so smaller values of three are to the LEFT; and we shade left, as depicted on the graph.
And that's it.
e-mail for more help!
Thanks :)

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