Concepts 1.1

1
Algebra 1
Chapter 6 Systems of Equations and
Inequalities
2
7/3/2015
Solving Systems by Graphing (y mxb)
Objective solve a linear system by graphing when
in slope-intercept form.
TSW solve a system of two linear equations in
two variables algebraically and are able to
interpret the answer graphically. Students are
able to solve a system of two linear inequalities
in two variables and to sketch the solution sets.
3
Notes

• Definitions

• Linear System (or System of Equations)

Two or more equations with the same variables

• Solution of a Linear System

The point where the two lines cross/intersect.
-Must make BOTH equations TRUE!

• Point of Intersection

The solution of the linear system.
4
Notes

• Solving a System of Equations by Graphing

1. Write each equation into slope-intercept
form.
What is m and b?
m move
b beginning
2. Graph both equations in the same coordinate
plane.
3. Find the point of intersection.
4. Check your answer.
- Plug that point into both equations and make
sure that it is true for both.
5
Notes
Solve the system by graphing.
Ex.
1) Put in slope- intercept form.
2) Graph the equations.
- Find m and b first.
3) Point of intersection?
4) Check answer!
6
Notes
Step 5- Check your answer.
x
y
7
Notes
Solve the system by graphing.
Ex.
Now you try.
1) Put in slope- intercept form.
2) Graph the equations.
- Find m and b first.
3) Point of intersection?
4) Check answer!
8
Notes
Step 5- Check your answer.
x
y
9
Notes
Solve the system by graphing.
Ex.
1) Put in slope- intercept form.
2) Graph the equations.
- Find m and b first.
3) Point of intersection?
4) Check answer!
10
Notes
Step 5- Check your answer.
x
y
11
Notes
Solve the system by graphing.
Now you try.
Ex.
1) Put in slope- intercept form.
2) Graph the equations.
- Find m and b first.
3) Point of intersection?
4) Check answer!
12
Notes
Step 5- Check your answer.
x
y
13
Notes
Solve the system by graphing.
Ex.
1) Put in slope- intercept form.
2) Graph the equations.
- Find m and b first.
3) Point of intersection?
4) Check answer!
14
Types of Solutions

• Number of Solutions for a Linear System

A
B
C
No solution
One solution
Infinite solutions
(Same Lines)
(Parallel Lines)
15
Types of Systems

• There are three possible outcomes when graphing
  two linear equations in a plane.
• One point of intersection, so one solution
• Parallel lines, so no solution
• Coincident lines, so infinite number of solutions
• If there is at least one solution, the system is
  considered to be consistent.
• If the system defines distinct lines, the
  equations are independent.

16
Linear Systems in Two Variables
Three possible solutions to a linear system in
two variables One solution coordinates of a
point No solutions inconsistent case Infinitely
many solutions dependent case
17
Solving Systems by Graphing
18
Class Work
Solve the system by graphing.
19
Thursday, February 6th
HOMEWORK Worksheet 6.1A
Rules for Homework

• Pencil ONLY.
• Must show all of your work.
• NO WORK NO CREDIT
• Must attempt EVERY problem.
• Always check your answers.