In Exercises 7–24, solve each system by graphing. Indentify systems with no solution and system with infinitely many solutions, using set notation to express their solution sets.
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EBK INTERMEDIATE ALGEBRA FOR COLLEGE ST
- Show all work to verify if the given point is a solution to the system of equations.arrow_forwardIn Exercises 3–6, solve each system by graphing. Identify systems with no solution and systems with infinitely many solutions, using set notation to express their solution sets. 3. x + y = 5 3x - y = 3 4. [3x – 2y = 6 16x – 4y = 12 3 y 6. [y = -x + 4 |3x + 3y = -6 5. 5h 2х — у %3D — 4arrow_forwardThree components are connected to form a system as shown in the accompanying diagram. Because the components in the 2–3 subsystem are connected in parallel, that subsystem will function if at least one of the two individual components functions. For the entire system to function, component 1 must function and so must the 2–3 subsystem |-------2-------| ---1------>| |----------> |-------3-------| The experiment consists of determining the condition of each component [S(success) for a functioning component and F(failure) for a nonfunctioning component]. a. Which outcomes are contained in the event A that exactly two out of the three components function? b. Which outcomes are contained in the event B that at least two of the components function? c. Which outcomes are contained in the event C that the system functions? d. List outcomes in C', A U C, B U C.arrow_forward
- Solve the linear system X₁ + x2 + x3 + x4 = 1 3x₁ + x2 + x3 — X4 = 5 5x1 x₂ + x3 = 5x4 = 3 x2 Describe the solution set geometrically.arrow_forwardSolve the linear system x1 + x2 + x3 + x4 = 1 3x1 + x₂ + x3 x4 = 5 5x₁x₂ + x3 - 5x4 = 3 Describe the solution set geometrically.arrow_forwardAn 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?arrow_forward
- Charlotte works at an electronics store as a salesperson. Charlotte earns a 10% commission on the total dollar amount of all phone sales she makes, and earns a 4% commission on all computer sales. Charlotte had twice as much in computer sales as she had in phone sales and earned a total of $162 in commission. Write a system of equations that could be used to determine the dollar amount of phone sales Charlotte made and the dollar amount of computer sales she made. Define the variables that you use to write the system.arrow_forward1) Describe the three possible solutions to a system of equations.arrow_forwardSolve by the method of your choice. Identify systems with no solution and systems with infinitely many solutions, using set notation to express their solution sets.arrow_forward
- Determine the value(s) of k such that the linear system has the indicated number of solutions.arrow_forwardFind all solution to the system of congruences.arrow_forward2. Describe the solution set in R³ of the linear system x₁ + 3x2 + 5x3 = = - 1, 2x1 + x₂ + 5x3 = 3, algebraically and geometrically (Fig. in R³). -arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage