For Exercises 13–16, solve the system. If a system has one unique solution, write the solution set. Otherwise, determine the number of solutions to the system and determine whether the system is inconsistent, or the equations are dependent. u + v + 2 w = 1 2 v − 5 w = 2 3 u + 5 v + w = 1
For Exercises 13–16, solve the system. If a system has one unique solution, write the solution set. Otherwise, determine the number of solutions to the system and determine whether the system is inconsistent, or the equations are dependent. u + v + 2 w = 1 2 v − 5 w = 2 3 u + 5 v + w = 1
Solution Summary: The author explains the steps for solving a system of three linear equations in three variables.
For Exercises 13–16, solve the system. If a system has one unique solution, write the solution set. Otherwise, determine the number of solutions to the system and determine whether the system is inconsistent, or the equations are dependent.
For Exercises 9–10, determine if the equation is linear or nonlinear. If the equation is linear, find the solution set.
−2x = 8
An important application of systems of equations arises in
connection with supply and demand. As the price of a product
increases, the demand for that product decreases. However, at
higher prices, suppliers are willing to produce greater quantities of
the product. Exercises 97–98 involve supply and demand.
97. A chain of electronics stores sells hand-held color
televisions. The weekly demand and supply models are
given as follows:
Number sold
Demand model
per week
N = -5p + 750
Price of television
Number supplied to
the chain per week N = 2.5p.
1apow hjddns
a. How many hand-held color televisions can be sold and
supplied at $120 per television?
b. Find the price at which supply and demand are equal. At
this price, how many televisions can be supplied and sold
each week?
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