Algebraic Word Problem#3 - Need Help Please

Question

Graph the system of inequalities presented here on your own paper, then use your graph to answer the following questions:

y < 2x − 7
y is greater than or equal to -1/2x +3

Part A: Describe the graph of the system, including shading and the types of lines graphed. Provide a description of the solution area. (6 points)

Part B: Is the point (3, −7) included in the solution area for the system? Justify your answer mathematically. (4 points)

Answer 1

Graph both lines.  Shade the region below the dotted line (2x - 7), and shade above the solid line (-0.5x + 3).  The overlapping shaded region is the solution to the system of inequalities.

 

If the point (3, -7) lies on the overlapping shaded region, then the point is a solution.  To justify it mathematically, simply plug in x=3 and x=-7 into the system.  The value of x and y must make both statements true to make point a solution.

 

-7 < 2(3) - 1                   true or false?

-7 ≥ -(1/2)(3) + 3            true or false?