1. I can solve a system of equations by graphing and using tables.
3-1 Linear Systems
Unit Objectives
Solve a system of equations graphically and algebraically.
Solve a system of linear inequalities.
Model situations with linear systems
Today’s Objective:
I can solve a system of equations by graphing and using tables.

2. If the sharks growth rate stays the same, at what age would they be the same length and how long will they be?

3. Solving a System using a graph:
System of Equations:
Two or more equations
Solution of a System:
Points that make all the equations true.
𝑦= 3 2 𝑥+4
1. Graph the equations
- change to y = mx + b
- graph the intercepts
2. Find the point of intersection
−3𝑥+2𝑦=8 3𝑥+2𝑦=−4
𝑦=− 3 2 𝑥−2
Calculator:
Put equations in [y =]
Adjust [window] to see intersection.
[2nd], [trace], [5] (intersection)
[enter], [enter], [enter]
(−2, 1)

4. Solving a System using a graph:
1. Graph the equations
2. Find the point of intersection
Solving a System using a graph:
𝑦= 1 2 𝑥−2
𝑥−2𝑦=4 3𝑥+𝑦=5
Calculator:
Put equations in [y =]
Adjust [window] to see intersection.
[2nd], [trace], [5] (intersection)
[enter], [enter], [enter]
𝑦=−3𝑥+5
Table:
Put equations in y =
[2nd], [graph]
Scroll to matching y values
(2, −1)

5. Classifying a system Consistent: has a solution
Inconsistent: has no solution
Independent: one solution
Dependent: infinite solutions
Same slopes
Different y-intercepts
Same slopes
Same y-intercepts
Different slopes
−2𝑥+4𝑦=6 −4𝑥+8𝑦=−12
= 𝑦=0.5𝑥+1.5 𝑦=0.5𝑥−1.5
Inconsistent

6. Graph on graph paper, then check on calculator.
x = years
y = length
𝑦=0.75𝑥+37
𝑦=1.5𝑥+22
If the sharks growth rate stays the same, at what age would they be same length and how long will they be?
3-1 p.138:7-13 odd, odd
Graph on graph paper, then check on calculator.
20 years and they will be 52 cm long

7. Extra word problems

8. System of Equations A local gym offers two monthly membership plans.
Visits
Plan A
Plan B
Plan A: One-time sign-up fee of $100 and charges $5 each time you use the gym. v v
10v 20
200
200
Plan B: No sign-up fee but charges $10 each time you use the gym.
When will the two plans cost the same?
First day lesson before section 2.2

9. Example 2
Josie makes and sells silver earrings. She rented a booth at a weekend art fair for $325. The materials for each pair of earrings cost $6.75, and she sells each pair for $23.
Write two equations to model the cost and income for Josie.
Create a table and graph to find the solution.
What does this solution mean?
x = Number of earrings
y = Dollars made or spent
The solution is where Josie will break even.
Earrings
Cost
Income x x
23x 20
460
460

10. Example 3
Edna leaves the trailhead to hike 12 miles toward the lake. Maria leaves the lake to hike towards the trailhead. Edna walks uphill at 1.5 miles/hour, while Maria walks downhill at 2.5 miles/hour.
write two equations to model both girls time and distance they are hiking. (Be sure define your variables) Create a table and graph to find the solution. What does this solution mean?
t = time spent hiking
d = distance traveled from trailhead
The solution is where Edna and Maria will meet.
time
Edna
Maria t
1.5t
12 – 2.5t 3
4.5
4.5