Algebra I: Chapter 7 Section 1
5B Graphing Systems of Equations Book
Examples: Graph each equation, find the intersection.
|y = x + 1 |y = 4x + 4 |y = 3x + 4 |
|y = 2x - 3 |y = 4x -5 |y = 3x + 4 |
| | | |
| | | |
| | | |
| | | |
| | | |
| | | |
| | | |
| | | |
There are 3 types of solutions to systems of 2 linear equations: _
• Inconsistent: The graphs of each equation have 0 solutions. They never intersect.
• Independent System: The system has one solution.
• Dependent System: the system has infinitely many solutions.
SUMMARY TABLE:
| |Intersecting Lines |Same Line |Parallel Lines |
|Graph of a System |[pic] |[pic] |[pic] |
|Number of Solutions | | | |
|Terminology | | | |
Practice Problems: Solve each system of equations. Make sure to show the slope intercept form for each.
| y = -x + 5 |y = -x -4 |y = 3 – x |
| | | |
|y = x – 3 |2x + 2y = -8 |2y = 8x – 14 |
| | |
|y = -x |y = 4 + 0.5x |
| | |
|y = 2x |x = -3 |
Graph the two equations using your CALCULATOR
STEP 1: Make sure each equation is in slope-intercept form
STEP 2: Press Y =, for Y1 write your first equation , for Y2 write your second equation
STEP 3: Press GRAPH
STEP 4: Press 2ND – CALC (Trace), Press 5 (Intersect), Press ENTER, ENTER, ENTER
Calculator will Output: Intersection: X = #, Y = # OR ERROR
Applying Systems of Equations to Word Problems
Suppose the following graphs represent ticket sales to the Carolina Panthers and Charlotte Bobcats games since 2000. And we were able to find the intersection of the lines.
x = years since 2000
y = number of tickets in thousands
What does the solution to this system of equations represent?
The number of years since 2000 and the number of tickets (in thousands) that are the same to both teams
For each of the following examples: create the system of linear equations, find the solution, and determine what the solution represents in the problem by graphing
6. The reading of daily newspapers is modeled by the linear equation y = -2.8x +170 and the reading of online newspapers is modeled by the linear equation y = 14.4x + 2. x represents the number of years since 1993 and y represents the average number of hours per year per person.
7: The width of a rectangle is 2 meters less than twice its length. What are the dimensions of a rectangle that has a perimeter of 40 meters.
8: Michael and Monica both want to buy a car. Monica has already saved $3500 and plans to save $445 per month until she can buy a car. Michael has already saved $2900 and plans to save $495 per month until he can buy a car. How long will it take Michael and Michelle to have saved the same amount and what is that amount?
-----------------------
y
x
y
x
y
x
Panthers Ticket Sales
Bobcats Ticket Sales
y
x
(7, 85)
................
................
In order to avoid copyright disputes, this page is only a partial summary.
To fulfill the demand for quickly locating and searching documents.
It is intelligent file search solution for home and business.