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# The Enormous State University History Department offers three coursesAncient, Medieval, and Modern Historyand the chairperson is trying to decide how...

x − y + z − u = .

Microsoft ? millionTime

Warner ? million

Yahoo ? million

Google ? million

4.Three market leaders in homeowners insurance in a state are State Farm, American Family Insurance Group, and Allstate. Based on data from a certain year, two relationships between the homeowners insurance percentage market shares are found to be as given below, where x, y, z, and w are the percentages of the market held by State Farm, American Family, Allstate, and other companies, respectively.

x = + 5y + z

z = − 2y + w

Given that the four groups account for the entire market, obtain a third equation relating x, y, z, and w, and solve the associated system of three linear equations to show how the market shares of State Farm, American Family, and Allstate depend on the share held by other companies. (Express your answer in terms of w, where x = x(w),

y = y(w),

and z = z(w).)

(x, y, z) = ?