PPT-Systems of Equations

Systems of Equations Finding all values of all variables that make the equations true What values make an equation true 7x3y12 What values make an equation true y 4x1 What values make all equations true. 4 Di64256erence Equations At this point almost all of our sequences have had explicit formulas for their terms That is we have looked mainly at sequences for which we could write the th term as for some known function For example if 1 3 then i 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 orgpublicinformationatefaqsgammaandexposurehtml It is a very good white paper by George Chabot CHP PHD that takes you from electric charge produced in the air by the photons to a usable equation and also explains where the simplified rule of thumb Rh Elimination . BINGO. Directions . Each person should have a BINGO board and an answer sheet. Each person must solve the system of equations on their own answer sheet. Once everyone has completed the problem, then the group can reveal the answer. Summary. Independent. The equations of a linear system are . independent. if . none. of the equations can be derived algebraically from the others. . Independence. When the equations are independent, each equation contains new information about the variables, and removing any of the equations increases the size of the solution set. . Hands-On Algebra with Fractions and Mixed Numbers. Connecting to Algebra . When you hear the word “algebra”, what do you think of?. What are some things you know about algebra?. How might you use algebra in real-life?. Parts of a chemical equation:. Reactants. : a substance present at the beginning of a chemical reaction. (Left side). Products. : a substance that is produced during a chemical reaction (Right Side). Substitution and Elimination. Elimination. Arrange the equations in STANDARD FORM. . . Your goal is to find a way to eliminate one of the variables so you can solve a one-variable equation.. . If you read from left to right . 10 . “is greater than “ . 5. . X. If you read from right to left . 5. . “is less than “ . 10. . X. If you read from left to right . 5. . “is less than “ . 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. . Ch. 1.6. Absolute Value Equations and Inequalities . EQ: How can you solve absolute value equations and inequalities? I Will solve absolute value equations and inequalities. . Bell Work. Solve the inequality. Graph the solution. . Introduction. This chapter gives you several methods which can be used to solve complicated equations to given levels of accuracy. These are similar to methods which computers and calculators will use, and hence can be used in computer programming. Examples:. . 1). . . x 3 = 15. . 2) p – 5 = 20. 3) 2d = 16. 4). . = 24.  . Multi-Step Equations. Examples—. 5). 2p 15 = 29. 6). 14 – 3n = -10. 7). 27 = -9(y 5). 8). 7a – 3a 2a – a = 16.  .  . 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.