Aim: How do we solve a system of linear equations using Agenda: graphing?
1/04/10 Do Now •Graphing
MiniLesson
•Solving Linear Systems By Graphing
Group work
•Past Regents questions
Share-out •Group Discussion
Summary •Discussion
Do Now (Quiz) 5 Minutes Graph the following equation: 2x + y = 4
Aim: How do we solve a system of linear equations using Agenda: graphing?
1/04/10 Do Now •Graphing
MiniLesson
•Solving Linear Systems By Graphing
Group work
•Past Regents questions
Share-out •Group Discussion
Summary •Discussion
•A system of linear equations is when you have two or more linear equations using the same variables. •The solution to the system is the point that satisfies ALL of the equations. The graphs of the system cross at that point. This point will be an ordered pair.
Aim: How do we solve a system of linear equations using Agenda: graphing?
1/04/10 There are three possibilities. Do Now •Graphing
MiniLesson
•Solving Linear Systems By Graphing
Group work
•Past Regents questions
Share-out •Group Discussion
Summary •Discussion
1. Intersecting Lines
(1,2)
• Solution is where the lines intersect (cross) • The solution of this system is (1, 2)
Aim: How do we solve a system of linear equations using Agenda: graphing?
1/04/10 Do Now •Graphing
MiniLesson
•Solving Linear Systems By Graphing
Group work
•Past Regents questions
Share-out •Group Discussion
Summary •Discussion
2. Parallel Lines
2 Slope = = 2 1 y-intercept = 2 y-intercept = -1
• Parallel lines have the same slope with different y-intercepts. • These lines never intersect! • Since the lines never cross, there is NO SOLUTION!
Aim: How do we solve a system of linear equations using Agenda: graphing?
1/04/10 Do Now •Graphing
MiniLesson
•Solving Linear Systems By Graphing
Group work
3. Coinciding Lines
2 Slope = = 2 1 y-intercept = -1
• These lines are the same! •Past Regents • Since the lines are on top of each other, questions Share-out there are INFINITELY MANY •Group SOLUTIONS! Discussion Summary • Coinciding lines have the same slope and •Discussion y-intercepts.
Aim: How do we solve a system of linear equations using Agenda: graphing?
1/04/10 Do Now •Graphing
MiniLesson
What is the solution of the system graphed below?
•Solving Linear Systems By Graphing
Group work
•Past Regents questions
Share-out •Group Discussion
Summary •Discussion
Intersection 1. 2. 3. 4.
(2, -2) (-2, 2) No solution Infinitely many solutions
Aim: How do we solve a system of linear equations using Agenda: graphing?
1/04/10 Do Now •Graphing
•Past Regents questions
Share-out •Group Discussion
Summary •Discussion
2. Find where the lines intersect 3. Check: 2x + y = 4 2(2) + (0) = 4 y=x-2 (0) =(2) – 2
4
Group work
1.Graph both equations
y=
•Solving Linear Systems By Graphing
2x + y = 4 y=x–2
+ 2x
MiniLesson
Find the solution to the following system:
y=
x–
2
(2, 0)
Aim: How do we solve a system of linear equations using Agenda: graphing?
1/04/10 Do Now •Graphing
MiniLesson
•Solving Linear Systems By Graphing
Group work
•Past Regents questions
Share-out •Group Discussion
Summary •Discussion
Using The Graphing Calculator To Solve Linear Systems 1. Write both equations in slope-intercept form 2. Press y= 3. Enter the first equation into y1 4. Enter the second equation into y2 5. Press Graph 6. *Zoom out to see where the lines cross* (Zoom, 3, Enter) 7. Press 2ND, TRACE, 5, ENTER, ENTER, ENTER 8. Record the value of x and y as your solution
Aim: How do we solve a system of linear equations using Agenda: graphing?
1/04/10 Do Now •Graphing
MiniLesson
•Solving Linear Systems By Graphing
Group work
•Past Regents questions
Share-out •Group Discussion
Summary •Discussion
Group Work
COMPLETE PasT REgEnTs QuEsTiOns
Aim: How do we solve a system of linear equations using Agenda: graphing?
1/04/10 Do Now •Graphing
MiniLesson
•Solving Linear Systems By Graphing
Group work
•Past Regents questions
Share-out •Group Discussion
Summary •Discussion
summar y
Explain how you can solve linear systems by graphing.
Aim: How do we solve a system of linear equations using Agenda: graphing?
1/04/10 Do Now
Let's review! There are 3 steps to solving a system using a graph.
•Graphing
MiniLesson
Step 1: Graph both equations.
Graph using slope and y – intercept or x- and y-intercepts. Be sure to use a ruler and graph paper!
Step 2: Do the graphs intersect?
This is the solution! LABEL the solution!
Step 3: Check your solution.
Substitute the x and y values into both equations to verify the point is a solution to both equations.
•Solving Linear Systems By Graphing
Group work
•Past Regents questions
Share-out •Group Discussion
Summary •Discussion