1. Topic-
Solving a Non linear system of equations.
 
2. Content-
Solving Non Linear System of equations in two variables using the method of addition/elimination.
 
3. Goals: Aims/Outcomes-
The students will be able to solve non linear systems by the method of addition/elimination.

 
4. Materials and Aids-
Overhead projector, white board and marker pens.
 
5. Procedures/Methods-

A. Introduction-

1.Warm up activity - Students solve a problem from the previous lesson topic which is solving non linear systems by the method of substitution.

Solve : x +2y = 0
(x-1)^2 + (y-1)^2 = 5
Once they are done, they come forward and start solving the problem on the board. Three students are then randomly called to explain the problem to the entire class.
Duration : 8 mins

 

B. Development-

We start by writing down the steps involved in solving a non linear system by the method of addition/elimination. We then write the first example. I demonstrate and model the first example :
4x^2 + y^2 = 13
x^2 + y^2 = 10

Step 1: Multiply the second equation by -1.
That is, -1x^2 - 1y^2 = -10

Step 2 : Add the resulting equation with the first equation and we get,

3x^2 = 3
x^2 = 1
x = 1, -1

Step 3 : We find y when x = 1 and x = -1 respectively by substituting the value of x in the second equation.
when x = 1,
(-1)^2 + y^2 = 10
y^2 = 9
y = 3, -3

Similarly, we find that when x = 1, y = 3 , -3

The solution is represented as a collection of ordered pairs within a set notation.

Therefore, the solution to the given system of equations is {(1,3),(1,-3),(-1,3),(-1,-3)}
Duration : 12 mins




 

C. Practice-

The students solve a similar example as guided practice.

Solve : 3x^2 + 2y^2 = 35
4x^2 +3y^2 = 48
Duration : 10 mins

If time permits, I plan to model another example in class which can be considered an extension of the substitution method studied in the previous lesson.

Solve: 2x + 3y = 36
xy = 54

 

D. Independent Practice-

The following problems are given as homework. The homework is also uploaded online in the teachers webpage along with the days lesson.

1. Solve: x ^2 + y^2 = 13
x^2 - y^2 = 5
2. x^2 - 4y^2 = -7
3x^2 +y^2 = 31
3. x^2 + y^2 = 25
(x -8)^2 + y^2 = 41
4. y^-x = 4
x^2 + y^2 =4

 

Closure-

I would check with all my students if they had any questions regarding the days lesson. The students usually raise their hands if they had a question and I would make sure I answer all of their questions to the best of my ability.
 

This Lesson Plan is available at (www.teacherjet.com)