Question

The unshaded region satisfies the inequalities
x+y x+y> b
Find the value of a and b.

Answer 1

find the values of a and b for the unshaded region that satisfies the inequalities x + y < a and x + y > b, we can consider the boundary lines for these inequalities.

1. For x + y < a, the boundary line is x + y = a.

2. For x + y > b, the boundary line is x + y = b.

Now, to find the values of a and b where the unshaded region lies between these lines, we need to determine the relationship between a and b.

Since the unshaded region is between the lines x + y = a and x + y = b, we can say:

b < a

So, the value of a is greater than the value of b, and you can represent this mathematically as a > b.

Answer 2

For the left dotted line, y = -x - 3, derived from c = -3 and m = -1. The right dotted line, y = -x + 5, establishes the boundary for x + y < 5 (a = 5).

Considering the left dotted line as y = mx + c, with the given condition 0 = -3m + c, solving for c yields c = -3. Simultaneously, the condition -3 = c results in m = -1. Substituting these values back into the equation, we find y = -x - 3, representing the left dotted line.

For the right dotted line, the equation 1 = -x + 5 is established. Solving for y, we get y = -x + 5. This line signifies the boundary for the inequality x + y < 5, leading to the conclusion a = 5.

In summary, the left dotted line is represented by y = -x - 3, with intercepts c = -3 and m = -1. On the right, the line is described by y = -x + 5, forming the boundary for the inequality x + y < 5, indicating a = 5.

This analysis encapsulates the derivation of the equations for the left and right dotted lines, unveiling their slopes, intercepts, and roles in defining the corresponding inequalities.

The question probable may be:

The unshaded region satisfies the inequalities

x+y<a

x+y> b

Find the value of a and b.