1. What is the solution of this system?
8x + 3y = -9 and -8x + y = 29

2. Graphing Linear Inequalities in One orTwo Variables

3. You graph inequalities the same way you graph lines
(Just pretend the inequality sign is an equal sign, and graph the line)
Changes with inequalities
Lines are sometimes dashed and sometimes solid
Shading needs to occur either above or below the line

4. If the sign is > or < the line will be dashed
Graphing an Inequality in Two Variables
If the sign is > or < the line will be dashed
If the sign is  or  the line will be solid

5. When shading, as a general rule…
If it is > or  then you shade above
If it is < or  then you shade below the line
However, we will always check our
shading with an ordered pair, as you
will see on the following examples

6. Picking points to help shade
If you get confused where to shade, then you should always pick a point to check. If possible, use (0,0). You will always shade the TRUE side.
So, when you put (0,0) into the inequality, if it makes the inequality TRUE, then that’s the side of the line that should be shaded.
If (0,0) lies ON the line that you have graphed, then choose another ordered pair that is clearly on one side of the line.
*see examples to make this more clear*

7. Graphing an Inequality in One Variable
Graph x < 2
Step 1: Start by graphing the line x = 2
Make it dashed since there’s
no equal sign
Since it has to be x < 2 we shade everything to the left of the line.
Pick (0,0) and see if it’s
true… 0 < 2 TRUE!
So we shaded correctly

8. Graphing an Inequality in One Variable
Sketch a graph of y  3
Graph y = 3
Pick (0,0)
again to
see if you
shaded
correctly
0  3
FALSE!
So you
should have
shaded away
from (0,0),
which you
did!
Solid line
since there is
an equal sign
Shade above
since you
see the
greater than
symbol

9. Graphing an Inequality in Two Variables
Sketch a graph of x + y < 3
Step 1: Put into slope intercept form
y < -1x + 3
Step 2: Graph y = -1x + 3
Make it dashed since <
Since it says <, shade below
Pick an ordered pair like (0,0)
to check our shading:
0 + 0 < < 3 TRUE!
So you should shade where
(0,0) is located, which you did!

10. Graphing an Inequality in Two Variables
Sketch a graph of 3x + 2y > 2
Step 1: Put into slope intercept form
2y > -3x + 2
y > -3/2x + 1
Step 2: Graph y = -3/2x + 1
Make dashed since >
Since it says >, shade above
Pick an ordered pair like (0,0)
to check our shading:
3(0) + 2(0) > > 2 FALSE!
So you should shade where
(0,0) is NOT, which you did!