1. 2 equations 2 Variables Graphically Substitution Elimination
Systems of equations
2 equations 2 Variables
Graphically
Substitution
Elimination

2. Solving a System
Getting the ordered pair that makes both equations true Where the two lines would intersect You could have: No solution – meaning they never intersect 1 solution they intersect once Infinite solutions – they are really the same line

3. Graphically Solve both equations for y Graph both of the lines
Plot y-int
Do slope from y-int
Connect with a line
3. Find point of intersection
This works well if lines intersect at an exact point

4. Example
Solve the following system graphically Both already solved for y so graph them They intersect at (1,-2) Answer should be an Ordered pair

5. Number of solutions
What would graph look like for No Solutions 1 Solution Infinite solutions
Equations?

6. Graphically
This is used a lot in word problems Determine which company is better to go with at a certain point and why, intersections tell you this.

7. Example
Your niece wants to have a birthday party on either McDonalds or Dave and Busters.
Given the information below set up a system of equations and graph them
McDonalds: The fixed cost to set up is $75 and $5 for each person attending. Write an equation in slope intercept form to represent this.
Dave and Busters: The fixed cost to set up is $50 and $10 for each person attending. Write an equation in slope intercept form to represent this.
Once you have them graphed answer the following questions.
At what number of guest is the cost equal? How do you know?
What is the difference in cost for 20 people to go to Dave and Busters vs McDonalds?
When is it better to go to Dave and Busters vs McDonalds and when is it better to go to McDonalds vs Dave and Busters?
You want to invite 24 people to the part. How much will it cost at each location?
You have a $250 limit on the cost of the party, how many people could you invite to each location?

8. Substitution
Solve one equation for a variable, look for a variable with a 1 in front of it or an even number
Substitute the expression you just solved for into the variable of the other equation
Solve for the remaining variable
Take value of variable and substitute it into the first equation
Check ordered pair in second equation
Write answer as an ordered pair

9. Example

10. Number of solutions
How do you determine how many solutions if not graphing No Solutions – when you solve you get 2 numbers that are not equal to each other 1 Solution x and y both equal in number, process works Infinite solutions – x=x, number equals itself

11. Solutions
Think back to the equations used for solving graphically If we solve them using substitution

12. Elimination
Add the equations together to cancel out one of the variables
Line up equations so variables are above one another
Determine what to multiply the equations by so when you add them one of the variables will cancel
Add the equations together
Solve for remaining variable
Sub in value of variable into original 1st equation and solve
Check answer in second equation
Write answer as an ordered pair

13. Example