PPT-Solve Linear Systems by Graphing

A System is a set of equations A Linear System is two linear equations two lines Solving a Linear System The point of intersection of the lines is called the solution. e Ax where is vector is a linear function of ie By where is then is a linear function of and By BA so matrix multiplication corresponds to composition of linear functions ie linear functions of linear functions of some variables Linear Equations Understanding the difference. Linear equations. These equations take the form:. . y. = . mx. + . b. . . m. is the slope of the line. . b. is the value of . y. when . x. = 0 . (the . y. - . By: Christine Berg. Edited By: VTHamilton. Linear Equation. An equation for which the graph is a line. Solution. Any ordered pair of numbers that makes a linear equation true.. (9,0) IS ONE SOLUTION. p. 41. Inequality Symbols. Less than. Greater than. Less than or equal to. Greater than or equal to. Not equal to. Linear Inequality. Inequality with one variable to the first power.. for example: 2x-3<8. University of Michigan – Dearborn Science Learning Center. Based on a presentation by James . Golen. Revised by Annette . Sieg. …. Introduction. Before using this module you must already understand the basics of graphing (e.g., identifying dependent and independent variables, plotting data points). . Recall from JC maths / science:. Speed and distance are scalars. We use the vector versions, velocity (. ) and displacement (. ):.  . 1. Solve Problems About Linear Motion. only works for constant (or average) velocity.. Solve by Graphing . Warm-up. Find the x-intercepts..  .  . Solutions to a Quadratic .  . The solutions or roots to a quadratic equation are . ___________________. (Also called . . ).  .  .  . By graphing. Definition. A system of linear equations, aka linear system, consists of two or more linear equations with the same variables.. x + 2y = 7. 3x – 2y = 5. The solution. The solution of a system of linear equations is the ordered pair that satisfies each equation in the system. . A boat traveled 210 miles downstream and back. The trip downstream took 10 hours. The trip back took 70 hours. What is the speed of the boat in still water? What is the speed of the current?. Solve by substitution. Contents. Problem Statement. Motivation. Types . of . Algorithms. Sparse . Matrices. Methods to solve Sparse Matrices. Problem Statement. Problem Statement. The . solution . of . the linear system is the values of the unknown vector . GSE Accelerated Pre-Calculus. Keeper 5. Gaussian Elimination. A . multivariable linear system . is a system of linear equation in two or more variables. . The substitution and elimination methods you have previously learned can be used to convert a multivariable linear system into an equivalent system in . 2. 8.1: First Order Systems. We now look at systems of linear differential equations.. One of the main reasons is that any nth order differential equation with n > 1 can be written as a first order system of n equations in n unknown functions..  .  . Solutions are found at the intersection of the equations in the system.. Types of Solutions. Section 8.1 – Systems of Linear Equations. Consistent System. One solution. Consistent System. Infinite solutions. Scientist interpret tables, graphs, and diagrams to locate data, examine relationships in the data, and extend those relationships beyond the data.. Reading graphs can be like reading a foreign language though. It come easy to some and very difficult to others..