Solving Non-Linear Equation
In this lesson, we will first learn the underlying principles of solving non-linear equations, helping students understand the reasoning behind each step. Next, we will go through the standard steps for solving typical equations, followed by equations involving two fractions, three fractions, and finally three special cases.
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Solving Non-Linear Equation - Basic Concepts
First, we are going to go thru the underlying principles when solving non-linear equations.
Let’s say we have the equation a times b is equal to 1.
Therefore, when a is equal to 1, b is equal to 1
Or we can say that a is equal to half and b is equal to 2.
Or we can also say that a is equal to one-fifth, and b is equal to 5. So as we can see, we have infinite number of solutions!
Now let’s say we want to solve another equation c time d is equal to zero.
First, we can conclude that C and D are factors of C times D.
And to solve this equation, C can be equal to zero, or D can be equal to zero. And we have a finite number of solutions, which in this case is 2 solutions since we have 2 factors, C and D!
And we have determined structural method to solving non-linear equation:
Step 1: The first step is to move all terms to the left, so that right hand side is equal to zero
Step 2: Factorise the algebraic expression on the left
Step 3: Equate each factor to zero
Step 4: Find all the solutions to each factor using the Algebra 1 technique
Solving Non-Linear Equation - Two Fractions
For non-linear fractional algebra with two terms, we can apply the following steps:
Step 1: Cross multiple to remove all the denominators
Step 2: Remove all the brackets by performing expansion
Step 3:Algebra on the left. Right hand side equal to zero
Step 4: Factorise left hand side algebraic expression
Step 5: Make factors equal to zero, to get the answer
Solving Non-Linear Equation - Three Fractions
For non-linear fractional algebra with three terms, we can apply the following steps:
Step 1: Multiple all the terms with the LCM to remove the denominator
Step 2: Remove all the brackets by performing expansion
Step 3: Algebra on the left. Right hand side equal to zero
Step 4: Factorise left hand side algebraic expression
Step 5: Make factors equal to zero, to get the answer
Solving Non-Linear Equation - Special Equations
In this video, we will go through three special cases of non-linear equations, learning how to apply the most suitable method for each situation to solve them effectively.