1. Topic-
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Solving a Non linear system of equations. |
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2. Content-
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Solving Non Linear System of equations in two variables using the
method of addition/elimination. |
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3. Goals: Aims/Outcomes-
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The students will be able to solve non linear systems by the method
of addition/elimination.
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4. Materials and Aids-
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Overhead projector, white board and marker pens. |
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5. Procedures/Methods-
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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
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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
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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
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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
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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. |
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