MIME-Version: 1.0 Content-Type: multipart/related; boundary="----=_NextPart_01C9223F.4213D5D0" This document is a Single File Web Page, also known as a Web Archive file. If you are seeing this message, your browser or editor doesn't support Web Archive files. Please download a browser that supports Web Archive, such as Microsoft Internet Explorer. ------=_NextPart_01C9223F.4213D5D0 Content-Location: file:///C:/9F341E43/M117Lesson9.1-9.2doc.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Lesson 9

Lesson 9.1 and 9.2F’08

 

Objectives:  To determine if an ordered pair is= a solution for a

        &= nbsp;             system of equations.

        =             To solve a system of linear equations graphically.=

        &= nbsp;            To classify a system of linear equ= ations in two

        &= nbsp;             unknowns.<= /p>

        &= nbsp;         =    To solve a system of equations using substitution.=

 

System of equations-A group of two or more equations.

 

A solutions for a syst= em of equations: An ordered set of numbers that makes all equations in the system true.=

 

EXAMPLE:  Determine whether each ordered pai= r is a solution to the system of equations.

 

1.  x + y =3D 11

     2x - 3y =3D -4    ( 6, 5)

 

 

 

2.  3x - 5y =3D 11

      4x + 3y = =3D 5       ( 2, = 1)

 

 

3.  7x - 9y =3D 76     &nbs= p; (7, -3)

     5x + 8y =3D 11

 

 

 

There are three possible cases for solving a system of two linear equations in two variables.

 

Case 1     consistent system A system of equations that has at least one solution.      &n= bsp;  

3D"[image]"

Case 2   inconsistent system  A system of equations that has no solution.

3D"[image]"

Case 3   dependent system   A system of equations that has and infinite number of solutions.

These are equations with identical graphs.  We write the

Solution like this:

<= ![endif]>3D"[image]"

Independent equations: Equations that have different graphs.

 

3D"[image]"3D"[image]"

         

 

 

 

Identify each of the following systems as:

          a.   Consistent or inconsistent a= nd

          b.   Dependent or independent

 

3D"[image]" 3D"[image]" 3D"[image]"

 

 

___________________&nb= sp;         ________________= ___        &= nbsp; ___________________

 

 

___________________&nb= sp;         ________________= __        &= nbsp;   ___________________

 

 

 

 

Solve the following equations by graphing them on the same axis.

 

1.  &n= bsp;  x + y =3D 5

        2x - y =3D 7

3D"[image]"

2.  x + y =3D 4

     y - x =3D 6=

 

3D"[image]"

 

If we want to solve a system of equations that has a fractional answer, solvin= g by graphing would not be accurate.

 

Another method of solving a system of equation is by substitution.

 

To solve a system of two equations by substitution:

1.  Isolate one of the variables in on= e of the equations.

2.  In the other equation, substitute = the expression you found in step 1 for that variable.

3.  Solve this new equation.

4.  Using one of the equations contain= ing both variables, substitute the value you found in step 3 for that variable = and solve for the value of the other variable.

5.  Check the solution in the original equations.

 

Example:  Solve the system of equations using substitution.

 

1.  2x +y =3D 10

=

     3x - y =3D 5

 

 

 

 

 

 

 

 

 

 

2.  5x + 6y =3D 2

     10x + 3y =3D -2<= o:p>

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

3.    y =3D -2x

      4x + 2y = =3D 0

 

 

 

 

 

 

 

 

 

 Set up a system of equations and us= e them to solve:

  1.  Patrick is twice as old as his sister, Sherry.  The sum of

       thei= r ages is 12.  How old are they?=

 

 

 

 

 

 

 

 

 

 

2.  The length of the Reflecting Pool = at the national Mall in Washington D.C. is 800 feet more than = ten times the width.  What are the dimensions if the perimeter is 4900 feet?

 

 

 

 

 

 

 

 

 

 

 

CW Worksheet 9.1-9.2

Homework Math XL  9.1 and 9.2

 

DUE BY_____________________

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