Question 83553
<font face = "TIMES NEW ROMAN" COLOR = "RED" SIZE = 7><b>SOLUTION BY EDWIN McCRAVY</font></b>

I am asking someone to please help me with my last 2 problems for my final which has to be in before 12 midnight. I do not understand what to do with
either one of these problems. Thanking you in advance. 

solve the following system of linear inequalities by graphing.
3x+4y<12
x+3y<6
y>0 
give the coordinates of the point graphed.
A)(-3,2)
B)(2,-3)
C)(3,-2)
D) (-2,3)
<pre><font size = 5><b>

Plug each one into all the inequalities to see 
if they are all true.
I'll skip around.

Let's try D first:

Substitute (x,y) = (-2,3)

Plug in        3x+4y < 12
        3(-2) + 4(3) < 12
             -6 + 12 < 12
                   6 < 12

That's true:

Plug in         x+3y < 6
         (-2) + 3(3) < 6
              -2 + 9 < 6  
                   7 < 6

Oh, oh, that's false. So the answer isn't (D).

Now let's try (B)

Substitute (x,y) = (2,-3)

Plug in        3x+4y < 12
        3(2) + 4(-3) < 12
              6 - 12 < 12
                  -6 < 12

That's true:

Plug in         x+3y < 6
         (2) + 3(-3) < 6
               2 - 9 < 6  
                  -7 < 6

That's true.

Plug in y > 0
       -3 > 0

Oh, oh, that's false. So the answer isn't (B).

Now let's try (C)

Substitute (x,y) = (3,-2)

Plug in        3x+4y < 12
        3(3) + 4(-2) < 12
              9 - 8 < 12
                   1 < 12

That's true:

Plug in         x+3y < 6
         (3) + 3(-3) < 6
               3 - 9 < 6  
                  -3 < 6

That's true.

Plug in y > 0
       -2 > 0

Oh, oh, that's false. So the answer isn't (C).

So let's try (A).
Let's see:

Substitute (x,y) = (-3,2)

Plug in        3x+4y < 12
        3(-3) + 4(2) < 12
              -9 + 8 < 12
                  -1 < 12

That's true:

Plug in         x+3y < 6
         (-3) + 3(2) < 6
              -3 + 6 < 6  
                   3 < 6

That's true.

Plug in y > 0
        2 > 0

That's true.  So they are all true!  So that
means (x,y) = (-3,2) is the only one of the 
4 that satisfies all three of the given
inequalities,making the correct choice (A).

Edwin</pre>