LJ UNIT 6 Maths Collage Algebra PDF

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Download LJ UNIT 6 Maths Collage Algebra PDF

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Linear systems are those that the graph is a straight line while the non-linear systems are those that does not form a straight line. The simplest linear system i can think of is the equation of the line in the form of y=mx + b where m is the slope and b is the y-intercept; while the simplest non-linear system i can think f is the equation of the parabola y=x^2. Linear relationship recommends that two variables are specifically relative to one other: multiplying in one causes the other to grow twofold as well. Framework of linear equation comprises of two or more direct equation that made up with more than one variable and likely more than one equation. Example: 2x + y = 15 3x − y = 5 The non-linear framework of equation may be a system where one of the variables has a exponent other than 1 and/or there's a product of factors in one of the conditions. Example: x2 - 2y2 = 2 xy = 2 in dealing with the concept of linear, it is important to understand the following. simple linear equation is of the form: y = mx + , A linear equation looks like a straight line when graphed, It has a constant slope value, The degree of a linear equation is always 1. The output of a linear system is directly proportional to its input. Non-linear systems, A simple non-linear equation is of the form: ax2 + by2 = c, A non-linear equation look like a curve when graphed. It has a variable slope value. The degree of a non-linear equation is at least 2 or other higher integer values. With the increase in the degree of the equation, the curvature of the graph increases. The input and output of a non-linear system is not directly related (Abramson, 2015). Here are some of the simplest linear and non-leaner equations x + y = 6 --------(1) x - 2y = 3 -------(2) Solving by elimination subtract equation (2) from (1) And for non-linear systems x + y = 1 ------(1) y = x2 - 5 ------(2) From equation (1) ; y = 1 - x -----(3) Put equation (3) into equation (2) 1 - x = x2 - 5, x2 - 5 - 1 + x =0, x2 + x - 6 = 0, -------(4)

Factorizing equation (4); and getting to your answer. In our day to day life, the situation that can be related to linear system is when you do jogging in the morning. It involves distance and time which can be plotted as points in cartesian plane. While the example of nonlinear system is when you stir your milk in the glass. It forms a parabola which is one of the graphs of a nonlinear system. To graph a linear system, you only need two points and connect them to make a straight line. In graphing nonlinear system like quadratic equation, you need to know its properties like vertex, zeros, and intercepts. Reference: Abramson, J. (2015, February 13). Algebra and Trigonometry. OpenStax. https://openstax.org/details/books/algebra-and-trigonometry....