1. Daily Essential Question:
How do I solve a system of Linear equations using the graphing method?

2. System of 2 linear equations:
2 equations with 2 variables (x & y) each.
Ax + By = C
Dx + Ey = F
Solution of a System –
an ordered pair, (x,y) that makes both equations true.

3. Ex: Check whether the ordered pairs are solutions of the system:
Ex: Check whether the ordered pairs are solutions of the system: x-3y= x+3y=10
(-5,0)
-5-3(0)= -5
-5 = -5
-2(-5)+3(0)=10
10=10
Solution
(1,4)
1-3(4)= -5
1-12= -5
-11 = -5
*doesn’t work in the 1st eqn, no need to check the 2nd.
Not a solution.

4. Solving a System Graphically
Graph each equation on the same coordinate plane.
If the lines intersect: The point (ordered pair) where the lines intersect is the solution.
If the lines do not intersect:
They are the same line – infinitely many solutions (they have all points in common).
They are parallel lines – no solution
(they have no points in common).

5. Ex 1: Solve the system graphically: y=3x-12 y=-2x+3
(3, -3)

6. Ex 2: Solve the system graphically: y=-x-1 y=8-x
No Solution

7. Ex 3: Solve the system graphically: x+y=-2 2x-3y=-9
**Put in Slope-Intercept form**
(-3,1)

8. Ex 4: Solve the system graphically: 3x-2y=6
**Put in Slope-Intercept form**
∞ many

9. Ex 5: Solve the system graphically: 2x-2y= -8 2x+2y=4
(-1,3)

10. Ex 6: Solve graphically: x-y=5 2x+2y=10
(5,0)

11. Setting Up Application Problems
Define variables
Write as a system of equations
Resort Costs: Resort A charges $70 per night, plus a one-time surcharge of $5. Resort B charges $65 per night, plus a one-time surcharge of $20. After how many nights will the total cost be the same?
x = number of nights
y = 70x + 5
y = 65x + 20
y = total cost

12. Work Schedule: x = hours as lifeguard x + y = 18 8x + 6y = 124
You worked 18 hours last week and earned a total of $124 before taxes. Your job as a lifeguard pays $8 per hour, and your job as a cashier pays $6 per hour. How many hours did you work at each job?
x = hours as lifeguard
x + y = 18
8x + 6y = 124
y = hours as cashier

13. You Try!! x = MC ?’s x + y = 20 4x + 6y = 100 y = Problem solving ?’s
A math test is to have 20 questions. The test format uses multiple choice worth 5 points each and problem solving worth 6 points each. The test has a total of 100 points. Write a system to determine how many of each type of question are used.
x = MC ?’s
x + y = 20
4x + 6y = 100
y = Problem solving ?’s

14. Homework
Finish Homework sheet!