Difference between revisions of "Linear Equations in Two Variables"
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==Concepts Learning Sessions== | ==Concepts Learning Sessions== | ||
| − | [https://www.youtube.com/watch?v=EwaIdkFXGJ8&feature=youtu.be/ | + | [https://www.youtube.com/watch?v=EwaIdkFXGJ8&feature=youtu.be/ Session # 1] |
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Before delving into the concepts of Linear Equations in two variables, its important to revisit the basics of Algebra - terms, expressions and | Before delving into the concepts of Linear Equations in two variables, its important to revisit the basics of Algebra - terms, expressions and | ||
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**Graphical Method | **Graphical Method | ||
**Algebraic Method : (Methods of Substitution and Elimination have been discussed in this session) | **Algebraic Method : (Methods of Substitution and Elimination have been discussed in this session) | ||
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| + | [https://youtu.be/yeLD_YqMBvA/ Session # 2] What are Determinants? | ||
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| + | In this session, a small introduction to Determinants has been made. Cramer's Rule to solve a system of linear equations require the knowledge of Determinants and the method of finding its value. This session would not be sufficient for in-depth knowledge in Determinants. | ||
| + | |||
| + | [https://youtu.be/nkZzvdOuRCM/ Session # 3] Cramer's Rule | ||
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| + | In this session, a method of solving a pair of linear equations in two variables using Cramer's Rule has been described. | ||
| + | |||
| + | ==Demonstration Sessions== | ||
| + | [https://youtu.be/OwDcL4AeELA/ Session # 1] How does the graphical representation of a linear equation in two variables ax+by+c=0 change when the coefficients a, b and c are changed. The rotation and the translation of the graphs has been demonstrated. You can also check what happens to the graph when 'c' becomes zero. | ||
==Problems== | ==Problems== | ||
[https://youtu.be/o_W1HimKLpw/ Problem Solving Session# 1] Solving a pair of linear equations in two variables using the method of "SUBSTITUTION" | [https://youtu.be/o_W1HimKLpw/ Problem Solving Session# 1] Solving a pair of linear equations in two variables using the method of "SUBSTITUTION" | ||
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[https://youtu.be/ARsDKQcLwVk/ Problem Solving Session# 2] Solving a pair of linear equations in two variables using the method of "ELIMINATION" | [https://youtu.be/ARsDKQcLwVk/ Problem Solving Session# 2] Solving a pair of linear equations in two variables using the method of "ELIMINATION" | ||
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| + | [https://youtu.be/uRQ0oTma1BM/ Problem Solving Session# 3] Solving a pair of linear equations in two variables using the method of "CROSS MULTIPLICATION" | ||
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| + | [https://youtu.be/Poblj9EJrAQ/ Problem Solving Session# 4] Word Problem on Area of a Rectangle | ||
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| + | [https://youtu.be/mfZryzdWLmk/ Problem Solving Session# 5] Consistency of a System of Linear Equations in Two Variables | ||
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| + | [https://youtu.be/P7xvDbr-Uwc/ Problem Solving Session# 6] Consistency of a System of Linear Equations in Two Variables | ||
| + | |||
| + | [https://youtu.be/eCM0e_FlDDM/ Problem Solving Session# 7] Solving a system of non-linear equations reducible to linear form | ||
| + | |||
| + | [https://youtu.be/u6uVt6KW3jk/ Problem Solving Session# 8] Word Problem on fractions. "The sum of the numerator and denominator of a fraction is 3 less than twice the denominator. If the numerator and denominator are reduced by 1, the numerator becomes half the denominator. Determine the fraction." | ||
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| + | [https://youtu.be/sl-M29Sg3P8/ Problem Solving Session# 9] Word Problem on numbers and digits. "A two digit number is 3 more than 4 times the sum of digits. If 18 is added to the number, the digits are reversed. Find the number." | ||
Latest revision as of 08:41, 18 April 2019
Concepts Learning Sessions
Before delving into the concepts of Linear Equations in two variables, its important to revisit the basics of Algebra - terms, expressions and
definition and types of Polynomials. In this session following topics have been covered:
- Terms and Expressions
- Polynomials and their types
- Linear Polynomials
- Linear Equations in two variables
- Why is a Linear Equation called so?
- Meaning of solution of a Linear Equation
- A pair of Linear Equations
- Methods of Solving a pair of Linear Equations.
- Graphical Method
- Algebraic Method : (Methods of Substitution and Elimination have been discussed in this session)
Session # 2 What are Determinants?
In this session, a small introduction to Determinants has been made. Cramer's Rule to solve a system of linear equations require the knowledge of Determinants and the method of finding its value. This session would not be sufficient for in-depth knowledge in Determinants.
Session # 3 Cramer's Rule
In this session, a method of solving a pair of linear equations in two variables using Cramer's Rule has been described.
Demonstration Sessions
Session # 1 How does the graphical representation of a linear equation in two variables ax+by+c=0 change when the coefficients a, b and c are changed. The rotation and the translation of the graphs has been demonstrated. You can also check what happens to the graph when 'c' becomes zero.
Problems
Problem Solving Session# 1 Solving a pair of linear equations in two variables using the method of "SUBSTITUTION"
Problem Solving Session# 2 Solving a pair of linear equations in two variables using the method of "ELIMINATION"
Problem Solving Session# 3 Solving a pair of linear equations in two variables using the method of "CROSS MULTIPLICATION"
Problem Solving Session# 4 Word Problem on Area of a Rectangle
Problem Solving Session# 5 Consistency of a System of Linear Equations in Two Variables
Problem Solving Session# 6 Consistency of a System of Linear Equations in Two Variables
Problem Solving Session# 7 Solving a system of non-linear equations reducible to linear form
Problem Solving Session# 8 Word Problem on fractions. "The sum of the numerator and denominator of a fraction is 3 less than twice the denominator. If the numerator and denominator are reduced by 1, the numerator becomes half the denominator. Determine the fraction."
Problem Solving Session# 9 Word Problem on numbers and digits. "A two digit number is 3 more than 4 times the sum of digits. If 18 is added to the number, the digits are reversed. Find the number."
