An artist wants to analyze the time that he spends creating his art. He makes oil paintings and watercolor paintings. [math]\,\,\,\,\,[/math]•[math]\,\,\,[/math] The artist takes 8 hours to paint an oil painting. [math]\,\,\,\,\,[/math]•[math]\,\,\,[/math] He takes 6 hours to paint a watercolor painting. [math]\,\,\,\,\,[/math]•[math]\,\,\,[/math] He has set aside a maximum of 24 hours per week to paint his paintings. [math]\,\,\,\,\,[/math]•[math]\,\,\,[/math] The artist then takes 2 hours to frame and put the final touches on his oil paintings. [math]\,\,\,\,\,[/math]•[math]\,\,\,[/math] He takes 3 hours to frame and put the final touches on his watercolor paintings. [math]\,\,\,\,\,[/math]•[math]\,\,\,[/math] He has set aside a maximum of 12 hours per week for framing and final touch-ups. Write a system of inequalities that represents the time the artist has to complete his paintings. Graph the solution.
[list=1] [*]Create the system of inequalities. Let [i]x[/i] = the number of oil paintings he makes. Let [i]y[/i] = the number of watercolor paintings he makes. [*]Graph the system on the same coordinate plane. [*]The solution is the overlapping shaded region; any points that lie within it are solutions to the system. [/list] This applet is provided by Walch Education as supplemental material for the [i]CCGPS Coordinate Algebra[/i] program. Visit [url="http://www.walch.com"]www.walch.com[/url] for more information on our resources.