MATH-Learning Journal Unit 6
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Jan 9, 2024
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Learning Journal Unit 6
The goal of this week's assignment was to think about linear and non-linear systems. Introduction to systems of equations, solving systems of equations by graphing, solving systems of equations by substitution, solving systems of equations in two variables by addition method, identifying inconsistent systems of equations containing two variables are the concepts (only the names) that I need to accommodate the concept of linear in my mind. Identifying inconsistent systems of Equations containing
three variables, expressing the solution of a system of dependent Equations containing three variables, using systems of Equations to investigate profits, solving systems of three Equations in three variables, expressing the solution of a system of dependent Equations containing three variables (Abramson, 2017).
Solving a system of Non-linear Equations using Substitution, solving a system of Non-linear Equations using Elimination, graphing a Non-linear Inequality, graphing a system of Non-linear Inequalities, Decomposing p(x) / Q(x) where Q(x) Has Repeated linear factors, Decomposing p(x) / Q(x) where Q(x) Has a No Repeated linear factors (Abramson, 2017).
Solving systems of equations in two variables using the addition method is the simplest linear system I can think of. "A third approach of solving systems of linear Equations is the addition method," states Abramson. We combine two terms with the same variables but opposing coefficients in this manner, resulting in a sum of zero" (2017, p. 880). Solving a system of non-linear equations using elimination is the simplest non-linear system I can think of. "Elimination is a lot simpler procedure when the system comprises only two Equations in two variables (a two-by-two – system), rather than a three-by-three – system, because there are fewer stages," according to the textbook (Abramson, 2017, p. 906).
The approach employed in the textbook will be the strategy I utilize to obtain the graph of non-linear systems. "Recall that the graph is presented with a dashed line when the inequality is bigger than, y > a, or less than, y a," adds Abramson. The graph is shown with a solid line when the inequality is higher than
or equal to y a, or less than or equal to y a. The graph will form regions in the plane, and we'll test each region for a solution; if one point in the region works, the entire region works," says the author (2017, p.
908). And the approach described in the textbook will be utilized to obtain the graph of linear systems.
Reference:
Abramson, J. (2017). Algebra and trigonometry. OpenStax, TX: Rice University. Retrieved from
OpenStax. (n.d.). Retrieved December 7, 2021, from https://openstax.org/details/books/algebra-and-trigonometry.
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