1. Systems of Equations and Inequalities
Algebra 1
Chapter 6
Systems of Equations and Inequalities

2. Solving Systems by Graphing (y = mx+b)
4/22/2018
Solving Systems by Graphing (y = mx+b)
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. 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!

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
One solution
No solution
Infinite solutions
(Parallel Lines)
(Same 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:
Consistent
Dependent
Inconsistent
One solution
Lines intersect
No solution
Lines are parallel
Infinite number of solutions
Coincide-Same line

18. Class Work
Solve the system by graphing.

19. HOMEWORK: Worksheet 6.1A Thursday, February 6th Rules for Homework
Pencil ONLY.
Must show all of your work.
NO WORK = NO CREDIT
Must attempt EVERY problem.
Always check your answers.