SOLUTION: Solve the following system of linear inequalities by showing work and graphing. x � 3y > 6 3x + 2y > 12 Can anyone offer any help on this problem?

Click here to see ALL problems on Linear-equations

Question 83464: Solve the following system of linear inequalities by showing work and graphing.
x � 3y > 6
3x + 2y > 12
Can anyone offer any help on this problem?

Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
Solve the following system of linear inequalities by showing work and graphing.
x � 3y > 6
3x + 2y > 12
--------------
solve eqch inequality for y, as follows:
y < (1/3)x-2
y > (-3/2)x+6
------------------
Now, graph the EQUALITY associated with each inequality:

------------------------
Each of these is a boundary of the corresponding INEQUALITY.
They are not part of the graph so should be drawn as dashed lines.
--------------------------
Now, determine where the half-plane INEQUALITY lies relative to
each boundary. How???
1st Pic a test point, like (0,0)
Substitute those values into the INEQUALTIY to determine if the
point is in the half-plane solution.
-------------------
Substituting in the 1st InEQUALITY you get 0<(1/3)x-2; 0<-2
That is false so the half-plane on the other side of y=(1/3)x-2
should be shaded.
-----------
Substituting in the 2nd INEQUALITY you get 0>(-3/2)*0+6
That is true so the half-plane on the side of y>(-3/2)x+6
which contains the test point is the half-plane graph of
y>(-3/2)x+6. That half-plane should be darkened.
---------------
the intersection of the two darkened half-plnes is the
graph of the solution set of the system of inequalities.
================
Cheers,
Stan H.