graphing an inequality

[boogie]

ok, i took my final exam, and passed the class and the test with
an A

only missed 2 questions.
the teacher gave me the test to keep

one of the questions

x+y-3<=0
y-2<=2x

i had to graph both equations and shade the areas
where the solutions lie.
couldn't do it.

any ideas where to start?

|-2x-4|>6 wasnt a problem x<-5 or x>1

i dont know,,,anyway ---happy halloween

DAN:evil:

 

[mmm4444bot]

x + y - 3 <= 0

y - 2 <= 2x

i had to graph both equations and shade the areas
where the solutions lie.
couldn't do it.

any ideas where to start?

Solve each inequality for y.

The equality sign in each result represents a solid lines on the graph (y=mx+b).

For the inequality parts, if you cannot read from the y-solved results which side to shade on each, pick a test value on either side of the line and substitute its coordinates for x and y to see whether you get a true statement.

The solution region is the overlap of the two shaded regions, as those points are the only points that satisfy both given inequalities.

|-2x-4|>6 wasnt a problem x<-5 or x>1

happy halloween

Not sure why you're posting non-problem, but if you would like to discuss it please start a new thread.

Cheers

 

[soroban]

Hello, boogie!

Ok, i took my final exam, and passed the class and the test with an A.
Nice going!

One of the questions I missed:

. . \(\displaystyle x+y-3\:\le\:0\)
. . \(\displaystyle y-2\:\le\:2x\)
Graph both equations and shade the solution area.

Solve for \(\displaystyle y\!:\;\begin{Bmatrix}y \:\le \: \text{-}x+3 \\ y \:\le\:2x+2 \end{Bmatrix}\)

If the sign is \(\displaystyle \le\), shade the region below the line.
If the sign is \(\displaystyle \ge\), shade the region above the line.

Graph the line \(\displaystyle y \:=\: \text{-}x+3\)
It has intercepts: .\(\displaystyle (3,0),\: (0,3)\)
Plot the points and draw the line.
Shade the region below the line.

Graph the line \(\displaystyle y \:=\:2x + 2\)
It has intercepts: .\(\displaystyle (\text{-}1,0),\: (0,2)\)
Plot the points and draw the line.
Shade the region below the line.

Your graph should look like this:

            * |  *
             3o *
              |**
             2o:::*
             *|:::::*
            *:*:::::::*
         -1*::|:::::::::* 3
     -----o:-:+:-:-:-:-:-:o------
         *::::|:::::::::::::*
        *:::::|:::::::::::::::*
              |