Plickers!!!Plickers!!! Remember your #Remember your # No writing/tearing/bendingNo writing/tearing/bending Always return where they belongAlways return where they belong Let’s have fun with this!Let’s have fun with this!

Bellwork (1 of 3)Bellwork (1 of 3)

Which of the following items was Which of the following items was owned by the fewest U.S. owned by the fewest U.S. homes in 1990?homes in 1990?A. home computerA. home computerB. CD playerB. CD playerC. cordless phoneC. cordless phoneD. dishwasherD. dishwasher

Q #2Q #2

What is the slope of y=2x+5?What is the slope of y=2x+5?

A.A. 55

B.B. 5/25/2

C.C. 2/52/5

D.D. 22

Q #3Q #3

What is the y-intercept of What is the y-intercept of y=2/3x-6?y=2/3x-6?

A.A. -6-6

B.B. 2/32/3

C.C. 66

D.D. 3/23/2

Solving Systems of Solving Systems of Equations by GraphingEquations by Graphing

Goals: ~Solve systems of Goals: ~Solve systems of equations by graphingequations by graphing

~Determine whether a system has ~Determine whether a system has 1, infinitely many, or no solutions1, infinitely many, or no solutions

Key TermKey Term

System of Equations: System of Equations: Two or more Two or more equations with the same variablesequations with the same variables

3 Possibilities…3 Possibilities…

One solutionOne solution

No SolutionNo Solution

Infinitely many Infinitely many solutions solutions same line for same line for

both eqnsboth eqns

Steps to solve by graphingSteps to solve by graphing

1.1. Put equations in slope-intercept Put equations in slope-intercept formform

2.2. Graph: Plot the y-intercept then Graph: Plot the y-intercept then follow the slope ( ) to get the follow the slope ( ) to get the next pointnext point

3.3. The intersection point is the The intersection point is the solutionsolution Note: You can check by plugging Note: You can check by plugging

your answer inyour answer in

run

rise

Basically…Basically…

1.1. Get in y=mx+b formGet in y=mx+b form

2.2. GraphGraph

3.3. Find intersectionFind intersection

Example 1: Solve by graphing. Example 1: Solve by graphing.

•Answer: 1. Both are already in slope-intercept form

•2. Graph. Remember: y-int first then use slope to get next point

•3. Find the intersection point. This is your solution.

Y= -x+3 Y= 3/2x-2

GraphGraph

Solution is (2,1)

TRY IT!TRY IT!Solve by graphing…Solve by graphing…

Y=x+2Y=x+2 Y=3x-2Y=3x-2

Solution:Solution:

(2,4)(2,4)

Example 2: Solve by graphingExample 2: Solve by graphing 2x+y = 52x+y = 5

x – y = 1x – y = 1 Answer: Write each equation in slope-Answer: Write each equation in slope-

intercept form.intercept form. 2x+y=5 --> 2x+y=5 -->

y=-2x+5y=-2x+5

x- y = 1 -->x- y = 1 --> -y=-x+1 --> y=x-1-y=-x+1 --> y=x-1

Graph. Graph. (Graph y-int then follow the (Graph y-int then follow the slope[rise/run] to get the next point)slope[rise/run] to get the next point)

The point where they cross is the solutionThe point where they cross is the solution

GraphGraph

(2,1) is the solution.

Answer:Answer:

They cross only once so the They cross only once so the solution is (2,1)solution is (2,1)

TRY IT!TRY IT!Solve by graphing…Solve by graphing…

2x-y= -52x-y= -5 -2x-y= -1-2x-y= -1

Answer:Answer:

(-1,3)(-1,3)

How to know how many answers How to know how many answers there are just by looking at the there are just by looking at the system of linear equationssystem of linear equations One Solution:One Solution:

Different slopeDifferent slope Infinitely many solutions:Infinitely many solutions:

Same equations (same slopes Same equations (same slopes and y-intercepts)and y-intercepts)

No Solution (parallel):No Solution (parallel): Same slope & different y-interceptSame slope & different y-intercept

Example 3: Without graphing, write whether Example 3: Without graphing, write whether there will be one solution, infinitely many there will be one solution, infinitely many

solutions, or no solutionssolutions, or no solutions

y = -x + 3y = -x + 3 2y = -2x + 62y = -2x + 6 Solution :Solution :

Put in slope-Put in slope-intercept formintercept form

Look at the Look at the slope and y-slope and y-intercept to get intercept to get solution.solution.

y = -x + 3y = -x + 3 y = -x + 3y = -x + 3

AnswerAnswer

They both make the same They both make the same graph, so there are infinitely graph, so there are infinitely many solutions!! many solutions!!

TRY IT!TRY IT!Without graphing, write whether there will be Without graphing, write whether there will be one solution, infinitely many solutions, or no one solution, infinitely many solutions, or no solutionssolutions

2a.2a. y = 3x + 2y = 3x + 2

y = 3x -5y = 3x -5

2b2b y = ½ x -6y = ½ x -6

y = 4x + 10y = 4x + 10

Mr. Monroe bought 2 lbs of cheddar cheese and 3 lbs of turkey. He paid $26.35. Ms. Stewart paid $18.35 for 1.5 lbs of cheese and 2 lbs of turkey. Write the system of equations.

Let’s look at each person separately…•Mr. Monroe:

• 2x+3y=26.35•Ms. Stewart

• 1.5x+2y=18.35

•How would I start to try and solve this by graphing?