1. Bell ringer 2-14-19 What do you remember about systems of equations…
What methods can you use to solve them?
What does the solution represent?

2. Systems of Equations & Inequalities
Thursday, February 14, 2019

3. Systems of Equations & Systems of Inequalities
A system of equations is a set of two or more equations with the same variable values. To solve, you must find the values for each variable that will satisfy all equations in the system.
A system of inequalities is a set of two or more inequalities with the same range of variable values. To solve, you must find the regions that overlap.

4. Solving Systems of Equations
1. Graph the equations and determine where they intersect.
2. Solve by substitution.
3. Solve by elimination.
4. Solve by matrices.

5. Solve by graphing…
Make sure it is written in slope-intercept form (y = mx + b).
Start with the y-intercept, and make a point on the y-axis.
Use your slope to find a second point.
positive slope: go up and right
negative slope: go down and left
4. Draw a line to connect the points.

6. Vocabulary review:
Consistent – a system of equations with one or more solutions
Inconsistent – a system of equations with no solution
Dependent System – a system of equations whose graphs are the same line
Independent System – a system of equations whose graphs are different

7. Solving Systems of Inequalities
You must GRAPH and see where they overlap.
Remember, > or < is a dotted line because the values on the line are NOT included; ≥ or ≤ is a solid line because the values on the line are included.
Remember, > or ≥ shade above; < or ≤ shade below.

8. “Acceptable” dating age
Half plus 7 rule

10. Examples
Suppose you have just enough coins to pay for a loaf of bread priced at $ You have a total of 12 coins, with only quarters and dimes. How many of each coin do you have? 1. 2. 3.

11. Examples 4. 5.
Bob makes $10 an hour for mowing lawns and $12 an hour for raking leaves. He cannot work more than 15 hours per week. Bob wants to earn at least $120 per week. (a) Write a system of inequalities that represents the total hours Bob can work and the amount of money he wants to make in a week. Identify your variables. (b) Graph the inequalities to find out how many hours Bob needs to work at each job.

12. Write and Graph Systems of Equations and Systems of Inequalities
Assignment
Write and Graph Systems of Equations and Systems of Inequalities

13. Exit Ticket Where is the answer when you graph a system of equations?
Where is the answer when you graph a system of inequalities?
What are the rules for graphing systems of inequalities?