For Exercises 7–12, decide whether or not the given points are solutions to the system of equations.
7.
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- For Exercises 15–22, solve the system by using the addition method. (See Examples 3-4) 15. 2x + 3y = 11 16. 3x + y² = 21 17. x - xy = 20 18. 4xy + 3y² = -9 2 + 4y = 8 4x - 2y = -2 -2x2 + 3xy = -44 2xy + y = -5 21. x = 1- y 9x - 4y? = 36 19. 5x - 2y2 = 1 20. 6x + 5y = 38 7x - 3y = 9 22. 4x = 4 - y? 16y = 144 + 9x? 2x - 3y = -4arrow_forwardShow all work to verify if the given point is a solution to the system of equations.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
- By setting up and solving an appropriate system of linear equations, determine whether there is a parabola that passes through the points (-1,2), (0, –1), and (1,3). 2.arrow_forwardUse a system of linear equations to find the parabola y = ax? + bx + c that passes through the points (-1,2), (0, 1), and (2,6). Show all of your work.arrow_forwardSolve the systemarrow_forward
- How does one determine whether an ordered pair is a solution of a given equation? Ex. 7x-8y=56; (0,56), (8,0)arrow_forwardThe owl population in a year n can be divided into juveniles, subadults andadults. Adults produce, on average, 0.4 juveniles each year. Approximately53% of juveniles survive to be subadults the next year, while 73% of subadultssurvive to become adults. Approximately 89% of the adult population survivesfrom one year to the next.1. Write down the equations for juveniles, subadults and adults in the year n+1 as functions of the juvenile,subadult and adult populations at year n. Explain all terms.2. Carefully explaining your notation and the terms, write down a matrix equation of the form pn+1 = Apn. 3. If there are 21 juveniles, 17 subadults and 53 adults this year, how many of each would we expect nextyear? 4. What is the equation that would describe the population in 5 years? (Do not calculate it!)arrow_forwardIs 0,5 a system of equationsarrow_forward
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