Unit+3+-+Systems+of+Equations

=Unit Vocab-=
 * ====**Systems of Equations-** One or more equations that use the same variable.====
 * ====**One Intersection**- Ordered Pair====
 * ====**No Intersection**- Parallel====
 * ====**Infinite Intersection**- Same Line====
 * ====**Graphing**- When you have a list of data.====
 * ====**Substitution**- A multi-step method for solving systems of equations involving the substitution of a solution for a variable====

=Graphing Method-=

Steps:
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 * 1) Plot points on a graph
 * 2) Look for where the lines intersect

For More Examples Look at :
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 * Burger-Rama Dolls Worksheet
 * Video games Assignment

=Substitution Method-=

Steps:

 * 1) Re-arrange the equation, in order so that one of the variables is by its self
 * 2) Sub the expression into the other equation
 * 3) Solve The equation
 * 4) Sub the answer back into either of the equations and solve for the second variable
 * 5) Write answers as an ordered pair (x,y)

Another Example:
//y// – 3//x// = 5 //y// + //x// = 3

//y// + //x// = 3 //y// + //x// – //x// = 3 – x //y// = 3 – //x// //y// – 3//x// = 5 (3 – //x//) – 3//x// = 5 3 – //x// – 3//x// = 5 3 – 3 – 4//x//= 5 – 3 – 4//x// = 2 //x// = 2/–4 = –½ //y// + //x// = 3 //y// + (– ½) = 3 //y// – ½ = 3 //y// – ½ + ½ = 3 + ½ //y// = 3½

//y// – 3//x// = 5 3½ – 3(–½) = 5 //y// – 3//x// = 5 3½ + 1½ = 5 3½ + (–½) = 3 5 = 5 3 = 3

Answer: (–½, 3½)
=Elimination Method-=

Steps-

 * 1) Arrange like terms into columns
 * 2) Multiply both equations by a number to obtain the variables opposites
 * 3) Solve for the remaining variable
 * 4) substitute solution into one of the original equations and determine solution for the remaining variable.media type="custom" key="7583667"

=More Examples-=

code //x + y = 11// //3x - y = 5//
 * 1. Problem: Solve the following system:

Solution:** Solve the first equation for //y// (you could solve for //x// - it           doesn't matter).

//y = 11 - x//

Now, substitute //11 - x// for //y// in the second equation. This gives the equation one variable, which earlier algebra work has taught you how to do.

//3x - **(11 - x)** = 5// //3x - 11 + x = 5// //**4x = 16**// //**x = 4**//

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Now, substitute //4// for //x// in           either equation and solve for //y//. (We use the first equation below.)

//**4** + y = 11// //**y = 7**//

The solution is the ordered pair, **(4, 7)**. code

**2//x// + 2//y// = 6** || **First, solve each equation for "//y// =".**
 * ** Solve graphically: ** || **4//x// - 6//y// = 12**
 * To solve a system of equations graphically, graph both equations and see where they intersect. The intersection point is the solution. ||
 * **4//x// - 6//y// = 12**

** slope = ** || ** 2//x// + 2//y// = 6 **
 * //y//-intercept = -2 **

** slope = -1 **
 * //y//-interce ** ** pt = 3 ** ||

=Practice Problems-=

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=Useful Links:= Graphing Method- @http://www.purplemath.com/modules/systlin2.htm Graphing Practice Worksheet Substitution Method-@http://cstl.syr.edu/fipse/algebra/unit5/subst.htm Elimination Method-[] More on Elimination Method- @http://mrpilarski.wordpress.com/2009/12/04/solving-systems-of-equations-using-the-elimination-method/ Practice material- []