Download 8-1 Systems of Linear Equations and Graphs.jnt

Math 10
Ch 8&9 Solving Systems of Linear Equations
Lesson 8-1
Lesson 8-1 Systems of Linear Equations and Graphs
Warmup:
Eric works on the 23rd floor of a building. It takes Eric 90 sec. To walk down the stairs to the 14th floor. Nathan works on
the 14th floor and needs to go up to the 30th floor. He knows it will take 40 sec by elevator if the elevator makes no
other stops.
Suppose both men leave their offices at the same time. Create a graph to model their travel. What is the point of
intersection and what does it represent? (textbook, page 425)
Terminology:
Point of Intersection: ______________________________________________________________________________
System of Linear Equations: _________________________________________________________________________
Satisfies an equation: ______________________________________________________________________________
Solution to a System of Linear Equations: ______________________________________________________________
Ex. #1 For which of the following systems is the point (−1,1) a solution?
a)
5x + 6 y = 1
6 x + 2 y = −3
b)
3x + 4 y = 1
5x − 3 y = −8
c)
3x − 4 y = −6
3x + 3 y = 1
d)
2x + 3y = 1
4x + 6 y = 2
Math 10
Ch 8&9 Solving Systems of Linear Equations
Lesson 8-1
Ex. #2 Find the solution to each of the following systems:
A
-4
-2
0
2
4
a)
B
10
14
18
22
26
A
-2
-1
0
1
2
B
30
28
26
24
22
b)
{(1, 2)(2,3)(3, 4)(4,5)}
{(2,1)(3, 2)(4,3)(5, 4)}
Solution: ___________
Solution: ___________
c)
Solution: _________
Ex. #3 Solve the following system graphically.
x+ y =5
3x + y = 3
Check your solution.
We can also solve the system in Ex. #3 using the graphing calculator.
a)
b)
c)
d)
e)
Isolate “y” in both equations
Graph the two equations as Y1 and Y2 (press Y= button on calculator)
Set the window to match the above graph (press Window and set XMAX, XMIN, YMAX and YMIN)
Graph the system (press Graph)
Find point of intersection (press 2nd Calc, Intersect)
Math 10
Ch 8&9 Solving Systems of Linear Equations
Ex. #4 Solve graphically:
Lesson 8-1
3
y = − x +8
2
2 x + 4 y = 16
Check your solution:
Ex. #5 Two different companies rent cars. Company A charges $10/day and $0.75 per km driven. Company B charges
$35 per day and $0.50 per km driven.
a)
Create a system of linear equations to model the rental charges.
b)
Solve the linear system graphically. What does the solution represent?
c)
Verify your solution.