SlideServe
Télécharger Obtenir Pro
Menu
Accueil Pro
Préférences
ApparenceLight Aide et commentaires
© SlideServe · v2026

Understanding and Solving Linear Systems of Equations

zuri avatar
zuri
12 diapositives · 269 Views · Jul 22, 2014

This guide explains the fundamentals of solving linear systems of equations, particularly in two variables. It discusses key concepts such as consistent, inconsistent, dependent, and independent systems. You will learn how to graph equations in slope-intercept form, find solutions through intersection points, and verify them algebraically. Additionally, the guide covers practical approaches to solving word problems by creating linear models of the scenarios. Examples and steps for finding solutions both algebraically and graphically are included to enhance understanding.

Understanding and Solving Linear Systems of Equations - slide 1
01 / 12Understanding and Solving Linear Systems of Equations
1 / 17

Télécharger la présentation

Understanding and Solving Linear Systems of Equations
Une image / un lien ci-dessous est fourni (tel quel) pour télécharger la présentation

Politique de téléchargement : le contenu du site vous est fourni TEL QUEL pour votre information et votre usage personnel ; il ne peut être vendu, concédé sous licence ni partagé sur d’autres sites sans l’accord de son auteur.Le contenu vous est fourni TEL QUEL, pour votre information et votre usage personnel uniquement. Téléchargez la présentation en cliquant sur ce lien. Lors du téléchargement, si vous ne parvenez pas à télécharger une présentation, l’éditeur a peut-être supprimé le fichier de son serveur.Pendant le téléchargement, si vous ne parvenez pas à obtenir une présentation, le fichier a peut-être été supprimé par l’éditeur.

F I N

Plus de contenu associé

Transcription de la présentation

  1. Solving Linear Systems • The solution of a system of equations in two variables is an ordered pair (x,y) that satisfies each equation. • Consistent – means that there is at least one solution • Inconsistent - if there are no solutions then the system is inconsistent • The two lines are parallel • Dependant – a consistent system with infinitely many solutions • The two lines are on top of each other • Independent – a consistent system with exactly ONE solution • **All this vocabulary only applies to linear systems

  2. Practice and Examples: • Graph each of the below and classify the system as consistent and independent; consistent and dependant or inconsistent: • Examples:

  3. Steps: • 1) Solve for y (put in y=mx+b form) to make graphing easier • 2) Graph each line by using slope intercept form: • Find the y-int • Count off the slope • 3) Look for places that the graphs intersect and list these as solutions • 4) Verify solutions algebraically by plugging in each part of the ordered pair solutions

  4. Solving Word Problems • Word Problems can be solved in the following manner • Create a linear model for the problem • Solve each linear equation for the same thing (what we do when we solve for y in the earlier problems) then set these equations equal to each other. • Examples: pg. 9 29 and 33

  5. Finding Solutions • Algebraically – solve for one variable, set equal and find solution • Graphically – graph and look for intersection points • Simple Examples: • Solve: a) 2x=8 • b) x-5=2 • c) 2x+5=x-1

  6. Solving Non-Linear Systems • Just like linear equations are solved by looking for the places that their graphs intersect; non-linear systems are also solved by finding intersection points. • Examples will be shown later….. • Solutions or intersection points can be found algebraically by setting each equation equal to each other. • Example – find the solution(s) for the below set of functions

  7. Practice: • Find the solution(s) for the following set of functions algebraically:

  8. Solving Non-Linear Systems • Example 1: • Use a graph to identify ordered pair solution(s) for the following set of equations

  9. Graph should look like this: Identify Solutions Check Algebraically

  10. Graph to find the solution for: • Example 2:

  11. Solution is (0,-2)

  12. Word Problem Practice Heather and Amanda each improved their yards by planting hostas and geraniums. They bought their supplies from the same store. Heather spent $187 on 12 hostas and 13 geraniums. Amanda spent $109 on 4 hostas and 11 geraniums. What is the cost of one hosta and the cost of one geranium?