Advanced Algebra / Trigonometry

Section 3-1Solving Systems of Equations by

Graphing

Target Goals

1) Solve systems of linear equations by graphing.

2) Write systems of linear equations.

System of Equations** Two or more equations with the same variables.

:Ex3

2 6

x y

x y

** To solve a system of equations with two variables, find the ordered pair that satifies both of the equations.

3x y 3y x

2 6x y

To graph the linear equation,

get it in form.y mx b

2 6y x

equations can be solved by graphing.Besides "guess and check", systems of

The "solution" is where they intersect.

3,0

3

0

x

y

When graphing two lines, one of three things can happen...

Solving Systems of Linear Equations by Graphing

Solve the system of equations by graphingExample 1

5 2 10

15 6 0

x y

x y

5 2 10x y 2 5 10y x

55

2y x

15 6 0x y 6 15y x

5

2y x

No Solution

Solve the system of equations by graphingExample 2

2 5 10

4 10 20

x y

x y

2 5 10x y 5 2 10y x

22

5y x

4 10 20x y 10 4 20y x

22

5y x

Infinity many

solutions (IMS)

Exit Slip

.A

.B

Target Goal: Solve system of linear equations by graphing.

.C

.D

2 5

3 4 0

y x

x y

4,3

2, 1

IMS

.A

.B

.C

.D

Target Goal: Solve system of linear equations by graphing.

2 1

2 6

y x

y x

1,4

2,3

IMS

Graphing Systems of Linear Equations on Graphing Calculator

Solve the system of equations by graphingExample 3

5

2 4

x y

x y

Solve the system of equations by graphingExample 4

2 0

3

x y

y

Solve the system of equations by graphingExample 5

4 3 12

6 4 1

x y

x y

Writing Systems of Linear EquationsExample 6A service club is selling copies of its holiday cookbook to raise funds for aproject. The printer's set-up charge is $200, and each book costs $2 to print.The cookbooks will sell for $6 each. How many cookbooks must the clubsell before it makes a profit?

Let number of books sold.x Let the number of dollars.y

200 2 Costx y 6 Incomey x

Profit occurs whenever income is greater than costs.

Graph this system on a graphing calculator.

Profit will occur when the club sells its b51st ook.

End

Advanced Algebra / Trigonometry

Section 3-1Solving Systems of Equations by

Graphing

Target Goals

1) Solve systems of linear equations by graphing.

2) Write systems of linear equations.

System of Equations** Two or more equations with the same variables.

:Ex3

2 6

x y

x y

** To solve a system of equations with two variables, find the ordered pair that satifies both of the equations.

When graphing two lines, one of three things can happen...

Solving Systems of Linear Equations by Graphing

Solve the system of equations by graphingExample 1

5 2 10

15 6 0

x y

x y

Solve the system of equations by graphingExample 2

2 5 10

4 10 20

x y

x y

Exit Slip

.A

.B

Target Goal: Solve system of linear equations by graphing.

.C

.D

2 5

3 4 0

y x

x y

4,3

2, 1

IMS

.A

.B

.C

.D

Target Goal: Solve system of linear equations by graphing.

2 1

2 6

y x

y x

1,4

2,3

IMS

Graphing Systems of Linear Equations on Graphing Calculator

Solve the system of equations by graphingExample 3

5

2 4

x y

x y

Solve the system of equations by graphingExample 4

2 0

3

x y

y

Solve the system of equations by graphingExample 5

4 3 12

6 4 1

x y

x y

Writing Systems of Linear EquationsExample 6A service club is selling copies of its holiday cookbook to raise funds for aproject. The printer's set-up charge is $200, and each book costs $2 to print.The cookbooks will sell for $6 each. How many cookbooks must the clubsell before it makes a profit?

Let number of books sold.x Let the number of dollars.y

Profit occurs whenever income is greater than costs.

Graph this system on a graphing calculator.