Answer to Question #220175 in Algebra for Rashmay

Question

Reflect on the concepts of linear and non-linear systems. What concepts (only the names) did you need to accommodate the concept of linear and non-linear systems in your mind? What are the simplest linear system and non-linear system you can imagine? In your day to day, is there any occurring fact that can be interpreted as linear systems and non-linear systems? What strategy are you using to get the graph of linear systems and non-linear systems?

Answer 1

To check some relevant concepts related to linear and non-linear system.

(1) To find the concepts (names) needed to accommodate the concept of linear and non-linear systems :

Complex, Additivity, Homogeneity, Continuous, Rational, Differentiation, Differential equation and Recurrence relation.

(2) To find the simplest linear and non-linear systems:

Linear system

x+y=1

2x+3y=6

Non-linear system

2x²+y=5

−x²+y=2

(3) To find day-day life examples of linear and non-linear systems:

Non-linear equations can be used to solve the situations of 

i. Calculate a space of area in the kitchen to know the microwave size

ii. In garden, to calculate the required space to make a small park for car which its length is known.

Linear equations can be used to solve the situations of 

i. In predicting profit in small businesses when one or more variables are known and at least one variable is dependent on the other. i.e if i knew a cost of starting up a project and I have x profit in the first month, I can predict the profits month to month.

(4) To find the strategies are using to get the graph of linear systems and non-linear systems:

i. Non-linear system:

To get a graph of a non-linear system, graph the first equation then graph the second equation and then try to determine whether the line intersects are parallel or are the same line by sketching the possible options for intersection of parabola and a line. Identify the solution, if the line intersect, & identify the point of intersection . If the lies are parallel, then that the system has no solution, and if the lines are the same the system has an infinite number of solutions.

ii. Linear system:

To get a graph of linear system, first find the x-intercept of the line. Then make y=0 and solve for x, then make x=0 and solve for y. Then find a third solution to the equation. Put the three points and make sure that they line up so it will help to draw the line.