Download presentation

Presentation is loading. Please wait.

1
Do Now Graph x = -2 x + 4y = 12

2
**Section 3.1 Solving Systems using tables and graphs**

What is a System of Equations? Solving Linear Systems – The Graphing Method Consistent Systems – one point (x,y) solution Inconsistent Systems – no solution Dependant Systems – infinite solutions Solving Equations Graphically

3
**Concept: A System of Linear Equations**

Any pair of Linear Equations can be a System A Solution Point is an ordered pair (x,y) whose values make both equations true When plotted on the same graph, the solution is the point where the lines cross (intersection) Some systems do not have a solution

4
**Why Study Systems of Equations?**

We will study systems of 2 equations in 2 unknowns (usually x and y) The algebraic methods we use to solve them will also be useful in higher degree systems that involve quadratic equations or systems of 3 equations in 3 unknowns

5
**A “Break Even Point” Example. A $50 skateboard costs $12. 50 to build,**

A “Break Even Point” Example A $50 skateboard costs $12.50 to build, once $15,000 is spent to set up the factory: Let x = the number of skateboards f(x) = x (total cost equation) g(x) = 50x (total revenue equation)

6
**Using Algebra to Check a Proposed Solution**

Is (3,0) also a solution?

7
**Estimating a Solution using The Graphing Method**

Graph both equations on the same graph paper If the lines do not intersect, there is no solution If they intersect: Estimate the coordinates of the intersection point Substitute the x and y values from the (x,y) point into both original equations to see if they remain true equations

8
**Approximation … Solving Systems Graphically**

9
**Practice – Solving by Graphing**

Consistent: (1,2) y – x = 1 (0,1) and (-1,0) y + x = 3 (0,3) and (3,0) Solution is probably (1,2) … Check it: 2 – 1 = 1 true 2 + 1 = 3 true therefore, (1,2) is the solution (1,2)

10
**Practice – Solving by Graphing**

Inconsistent: no solutions y = -3x (0,5) and (3,-4) y = -3x – 2 (0,-2) and (-2,4) They look parallel: No solution Check it: m1 = m2 = -3 Slopes are equal therefore it’s an inconsistent system

11
**Practice – Solving by Graphing**

Consistent: infinite sol’s 3y – 2x = 6 (0,2) and (-3,0) -12y + 8x = -24 (0,2) and (-3,0) Looks like a dependant system … Check it: divide all terms in the 2nd equation by -4 and it becomes identical to the 1st equation therefore, consistent, dependant system (1,2)

12
**Summary of Section 3.1 Solve Systems by Graphing Them Together**

Graph neatly both lines using x & y intercepts Solution = Point of Intersection (2 Straight Lines) Check by substituting the solution into all equations Cost and Revenue lines cross at “Break Even Point” A Consistent System has one solution (x,y) An Inconsistent System has no solution The lines are Parallel (have same slope, different y-intercept) A Dependent System happens when both equations have the same graph (the lines have same slope and y-intercept)

13
Homework pg Homework: P. 138 #7,9,13,14,29,31,33,38,39,40,41,53,54 Challenge: #48

14
What Next? Present Section 3.2 Solving Systems Algebraically

Similar presentations

Presentation is loading. Please wait....

OK

Chapter 13 Section 2 Solutions of Systems of Equations.

Chapter 13 Section 2 Solutions of Systems of Equations.

© 2018 SlidePlayer.com Inc.

All rights reserved.

To ensure the functioning of the site, we use **cookies**. We share information about your activities on the site with our partners and Google partners: social networks and companies engaged in advertising and web analytics. For more information, see the Privacy Policy and Google Privacy & Terms.
Your consent to our cookies if you continue to use this website.

Ads by Google

Ppt on revolt of 1857 in india Ppt on tens and ones for grade 1 Ppt on management by objectives definition Ppt on nervous system Ppt on ac and dc servo motor Free download ppt on minerals and energy resources Ppt online downloader from youtube Ppt on history of atomic structure Ppt on uniform and nonuniform motion Ppt on brand marketing