Nash

media type="custom" key="6252125" = __**Vocabulary**__ = = = System of Linear Equations - Two or more linear equations using the same variables. Solution of the System of Linear Equations - Any ordered pair in a system that makes all the equations of that system true. No Solution - When the graphs of the equations in a system are parallel with no point of intersection. Infinitely Many Solutions - The number of solutions of a system of equations in which the graphs of the equations are the same line.

=media type="custom" key="6246863"= = __Examples__ =

media type="custom" key="6247027"

__//**1. Solving Systems of Equations by Graphing**//__
2y + 6 = 4x 3y = 3x - 3 //__**Step 1:**__// Turn your equations into y-intercept form, y = mx + b

2y + 6 = 4x 2y + 6 - 6 = 4x - 6 2y = 4x - 6 2y/2 = 4x/2 - 6/2 y = 2x - 3 - - - - - - - - - - - - - - - - - - - 3y = 3x - 3 3y/3 = 3x/3 - 3/3 y = x - 1

//__**Step 2:**__// Graph both equations //(See Above Image)// The two equations intersect at **(2,1)**. That is the solution.


 * //__Step 3:__//** Check your solution from the original equation

2y + 6 = 4x, (**2**,**1**) 2(**1**) + 6 = 4(**2**) 2 + 6 = 8 8 = 8 - - - - - - - - - - - - - - - - - - - 3y = 3x - 3, (**2**,**1**) 3(**1**) = 3(**2**) - 3 3 = 6 - 3 3 = 3

//__**2. Problem S**__////__**olving**__//
//Suppose you are testing two fertilizers on bamboo plants A and B, which are growing under identical conditions. Plant A is **6 cm tall** and growing at a rate of **4 cm/day**. Plant B is **10 cm tall** and growing at a rate of **2 cm/day**. __On what day__ and __how tall__ will they be when they both reach the __same height__?//

[[image:http://naturallyadvanced.files.wordpress.com/2009/11/bamboo.jpg width="239" height="178" caption="How tall is the bamboo?"]]
Let y = plant height Let x = days

Plant height is the initial height plus the daily growth per day

Plant A: y = 6 + 4x Plant B: y = 10 + 2x

//__**Step 1:**__// Put the two equations into y-intercept form, y=mx+b Plant A: y= 4x + 6 Plant B: y= 2x + 10


 * //__Step 2:__//** Graph both equations


 * The two equations intersect at (2 days, 14 cm) so in 2 days both plants will be 14 cm.**

//__3. Systems of Equations with No Solutions__//
media type="custom" key="6247053" width="80" height="80" The two equation's lines are parallel, therefore the system has no solution.

__//4. Systems of Equations with Infinitely Many Solutions//__
media type="custom" key="6247061" width="80" height="80" The two equations are on the same line, therefore the system has infinitely many solutions.