Consider the system of equations: Solve by graphing. Paste your graph below.
Consider the system of equations: Solve by substitution. Show ALL your work.
Consider the system of equations: Solve by elimination. Show ALL your work.
Which method do you prefer? Explain your answer.
Change the coefficient of y in the first equation so that the system has infinitely many solutions.
Fishing Limits Unit 4: Linear Equations,
Functions and Inequalities
I Can… ● Use linear equations to solve real-life problems. ● Solve linear equations by graphing. ● Use systems of linear equations to solve real-life problems. ● Solve systems of linear equations by graphing.
Mathematically proficient students apply the mathematics they know to solve real-life problems using systems of linear equations.
How will you be graded?
Your grading rubric is here.
K&T: 30 points
Written Communication: 10 points
Agency: 10 points
Collaboration: 20 pointshttps://www.google.com/url?q=https://docs.google.com/document/d/1_Cl2AGsyD3KHs9NthJ4NpSuxaMuqBknqzBtZvqiPLU4/edit?usp%3Dsharing&sa=D&source=editors&ust=1617170555399000&usg=AOvVaw1Seaf45h5xuEt2160CRqym
In this task, students will solve problems involving populations of fish by applying their knowledge of graphing and solving systems of linear equations.
A fishery is an area with the specific purpose of controlling fish populations for commercial or recreational fishing. Population dynamics describe how a fish population changes over time. The population is changed by birth, death, and migration of fish. While the supply of fish (population growth) can be modeled with a linear equation, so can the demand of fish (the amount caught). In one commercial venture, fishermen recorded their daily catch in an ocean fishery.
Using their data, the demand model for the total number y of fish caught for x days is y= 349x + 50
What is the meaning of the slope in this model? What is the meaning of the y-intercept?
Write an equation to model the fish population y in a fishery that has a linear growth rate of 40 new fish each season x, and an initial population of 1250 fish.
After how many seasons will the population reach 1690 fish?
Write an equation for a second fish population that grows by 60 new fish each season with an initial population of 1100 fish.
After how many seasons will they have the same population?
Paste your graph here. Use this website.https://www.google.com/url?q=https://www.desmos.com/calculator/2rnqgoa6a4&sa=D&source=editors&ust=1617170555414000&usg=AOvVaw2nqxrGcgkp_joqiw7KKQRz
One species of fish in a fishery had an initial population of 255 fish and after 9 seasons, the population had grown to 480 fish. A second species that was being overfished started with an initial population of 450 fish, and after the same 9 seasons, it had a new population of 90 fish.
Assuming a linear growth, write the equations for the population of each species.
Graph your equations in the coordinate plane. Find the point in the graph which represents when the two populations will have the same number of fish.
After how many seasons will the second population be eliminated?
Paste your graph here. Use this website.https://www.google.com/url?q=https://www.desmos.com/calculator/2rnqgoa6a4&sa=D&source=editors&ust=1617170555419000&usg=AOvVaw3fyK9UAE9Nql8o0YWZGCK8
Yield is the total number of fish caught each year. Maximum sustainable yield is the total number of fish you can catch without harming the population.
You are given a fish population that is described by the equation y = 126x + 745 and another fish population being overfished as described by the equation 33x + y = 1699 where x is the number of years and y is the number of fish.
After how many years will these two fish populations be equal?
Graph your equations in the coordinate plane.
Paste your graph here. Use this website.https://www.google.com/url?q=https://www.desmos.com/calculator/2rnqgoa6a4&sa=D&source=editors&ust=1617170555425000&usg=AOvVaw0BBls5YfOaikh9deAp-tIj