PPT-Systems of Equations

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. 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 using Elimination. Steps:. 1. Place both equations in Standard Form, A. x . + B. y . = C.. 2. Determine which variable to eliminate with Addition or Subtraction.. 3. Solve for the variable left.. I.3 Variables, expressions, and equations. Objective. Essential Question. Key Vocab. To translate words into algebraic expressions and equations. In what order are the terms written in the expression “less than?” (i.e. 5 less than 4). b. y. Tammy Wallace. Varina High School. What is a System of . Inequality?. A SYSTEM OF EQUATIONS is: . SOLUTIONS . to . a SYSTEM . OF . INEQUALITIES are. :. two or more . linear inequalities . with . 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?. Unit 3. What are . parametrics. ?. Normally we define functions in terms of . one . variable. – . for example, . y . as a function of x. . . Suppose in a graph, each (x, y) depended on a . third variable . Problem 1. There are 25 toys in a playground. . The toys are either bicycles (2 wheels) or tricycles (3 wheels). . In total in the playground there are 61 wheels. . How many bicycles are in the playground?. 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. . Standards 8-10. Graphs of Quadratic Functions . U- Shaped Graph . Vertical y=x. 2. or Horizontal x=y. 2. Positive Negative . Summary: The of a Quadratic Function is U shaped. . Positve. 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. 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. Net ionic equations are useful in that they show only those chemical species directly . participating in . a chemical . reaction. The keys to being . able to . write net ionic equations are the ability to recognize monatomic and polyatomic ions, .