Daily Essential Question:

How do I solve a system of Linear equations using the graphing method?

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.

Ex: Check whether the ordered pairs are solutions of the system:

x-3y= -5-2x+3y=10

A. (1,4)1-3(4)= -51-12= -5-11 = -5*doesn’t work in the 1st

eqn, no need to check the 2nd.

Not a solution.

B. (-5,0)-5-3(0)= -5-5 = -5

-2(-5)+3(0)=1010=10

Solution

Solving a System Graphically

1. Graph each equation on the same coordinate plane.

2. If the lines intersect: The point (ordered pair) where the lines intersect is the solution.

3. If the lines do not intersect:a. They are the same line – infinitely many

solutions (they have all points in common).

b. They are parallel lines – no solution (they have no points in common).

Ex 1: Solve the system graphically:y=3x-12y=-2x+3

Ex 2: Solve the system graphically:y=-x-1y=8-x

Ex 3: Solve the system graphically:x+y=-22x-3y=-9

**Put in Slope-Intercept form**

y x 2 2

y x 33

Ex 4: Solve the system graphically:3x-2y=6

-6x+4y=-12

**Put in Slope-Intercept form**

3y x 3

2

3y x 3

2

Ex 5: Solve the system graphically: 2x-2y= -8

2x+2y=4y x 4 y x 2

Ex 6: Solve graphically: x-y=52x+2y=10

y x 5 y x 5

Setting Up Application Problems

1. Define variables2. 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?

y = 70x + 5 y = 65x + 20

y = total cost

x = number of nights

Work Schedule:

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 + y = 18 8x + 6y = 124

x = hours as lifeguardy = hours as cashier

You Try!!

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 + y = 20 4x + 6y = 100

x = MC ?’sy = Problem solving ?’s

Homework

Finish Homework sheet!