`-yle 6x-2200`
`3y ge 9x -1500`
Given the system of inequalities above, if point (a,b) lies within the solution set, what is the minimum possible value of b ?

Explanation

To solve the given system of inequalities and find the minimum possible value of \( b \), we will follow these steps:

### Step 1: Rewrite the inequalities
The given inequalities are:
1. \( -y \leq 6x - 2200 \)
2. \( 3y \geq 9x - 1500 \)

We will rewrite these inequalities in terms of \( y \):
1. From \( -y \leq 6x - 2200 \), we can multiply both sides by -1 (remember to reverse the inequality):
\[ y \geq 2200 - 6x \]

2. From \( 3y \geq 9x - 1500 \), we can divide both sides by 3:
\[ y \geq 3x - 500 \]

### Step 2: Set up the equations for the minimum value of \( b \)
Let \( a \) represent \( x \) and \( b \) represent \( y \). The inequalities we have now are:
1. \( b \geq 2200 - 6a \) (Inequality 1)
2. \( b \geq 3a - 500 \) (Inequality 2)

To find the minimum possible value of \( b \), we will set these inequalities as equalities:
1. \( b = 2200 - 6a \)
2. \( b = 3a - 500 \)

### Step 3: Solve the equations
Now, we will set the right-hand sides of the two equations equal to each other:
\[ 2200 - 6a = 3a - 500 \]

### Step 4: Rearranging the equation
Rearranging the equation gives:
\[ 2200 + 500 = 3a + 6a \]
\[ 2700 = 9a \]
\[ a = \frac{2700}{9} = 300 \]

### Step 5: Substitute \( a \) back to find \( b \)
Now we can substitute \( a = 300 \) back into either equation to find \( b \). Let's use the second equation:
\[ b = 3(300) - 500 \]
\[ b = 900 - 500 = 400 \]

### Conclusion
Thus, the minimum possible value of \( b \) is:
\[ \boxed{400} \]