Precal lesson - Nonlinear Equations

Hey Everyone , Its Deep

In our Today's Class , first we did Systems of Equations Word Problems . Mr.p told us and tell us how to do the sum .Here is the example that Mr.P told us on Smart board.

   Example:-3. The sum of the digits of a certain two digit number is 12. Reversing the digits decreases the number by 54. What is the number?

  Solution:-

                 we let the first number be x and second number be y .

so , according to the statement 

the first equation will be 

                       x+y=12

 and by understanding the statement 

                  10y+x+54=10x+y

                   10y-y+x-10x =-54

so by solving the statement 

             we got the second equation  and it will be

                              9y-9x =-54

by solving this both equations by any one of the method 

                       we got ,

        18y =54 

              y=3

so by putting the value 

we got 

                x+y=12 

                   x+3=12 

                   x=9 

so the number will be 93

                        And then after this we did systems of nonlinear equations and it includes mostly the stuff we did in the beginning of this chapter and some stuff related to conics .

        The General Equation for a Conic Section:

Ax² + Bxy + Cy² + Dx + Ey + F = 0

              The related stuff here i m showing u 

                         

• Solve the system of nonlinear equations:
y = x² x² + (y – 2)² = 4
From the form of the equations, you should know that this system contains a parabola and a circle.

According to the graph, there should be three solutions to this system: The solution at the origin is a "neat" one, but the other two intersection points may be messy.

From the first equation, I think I'll plug in "y" for "x²" in the second equation, and solve:
x² + (y – 2)² = 4 y + (y – 2)² = 4 y + (y² – 4y + 4) = 4 y ² – 3y = 0 y(y – 3) = 0 y = 0,  y = 3
Now I need to find the corresponding x-values. When y = 0:
y = x²0 = x²0 = x
(This is the solution at the origin that we'd been expecting.) When y = 3:
y = x²3 = x²±sqrt(3) = x
Then the solutions are the points , (0, 0), and . so if u want to gather more information including that stuff so there the some websites.                               http://www.brightstorm.com/math                                  
• Solve the following system:
y = 2x² + 3x + 4 y = x² + 2x + 3

As before, I'll set these equations equal, and solve for the values of x:		2x2 + 3x + 4 = x2 + 2x + 3 x2 + x + 1 = 0
Using the Quadratic Formula:
But I can't graph that negative inside the square root! What's going on here? Take a look at the graph:

The lines do not intersect. Since there is no intersection, then there is no solution. That is, this is an inconsistent system. My final answer is: no solution: inconsistent system.
                                       here is the stuff that related we did 
                                                             http://www.youtube.com/watch and even u can take the help from the website khan academy .org
                                                                                        so we only one day left for winter break.
                     merry christmas 
                                            to all 
                                                                  bye and i will see u tomorrow