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Simultaneous Linear Equations | Class 9th Math Full Exercise 5A | R.S.Aggarwal Math | ICSE MATH

ICSE MATH - Manish Kaushik・2 minutes read

Chapter 5 focuses on Simultaneous Linear Equations and methods like substitution, elimination, and cross multiplication, highlighting the importance of understanding and verifying solutions for accurate results. The text provides detailed steps and practical examples to guide the process of solving equations using different methods, emphasizing clarity, simplicity, and accuracy throughout.

Insights

Linear equations consist of variables (like x, y) and coefficients (like 3, 4, 9), each with specific numbers.
Methods to solve linear equations include substitution, elimination, and cross multiplication, with the choice of method depending on the question.
Verifying answers after solving linear equations is crucial for accuracy and understanding mathematical concepts.
Understanding and applying mathematical methods correctly, such as substitution and elimination, are essential for solving equations effectively.

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What are linear equations?
Mathematical equations with variables and coefficients.

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Summary

00:00

Solving Linear Equations: Methods and Verification

Chapter 5 of class ninth on Channel Esse Math focuses on Simultaneous Linear Equations.
Linear equations consist of variables (like x, y) and coefficients (like 3, 4, 9).
Each linear equation has a specific number of variables and coefficients.
Methods to solve linear equations include substitution, elimination, and cross multiplication.
The elimination method involves eliminating one variable by manipulating equations.
Cross multiplication is another method used to solve linear equations.
The choice of method (substitution, elimination, or cross multiplication) depends on the question.
Applying the correct method is crucial for solving linear equations accurately.
After solving linear equations, verifying the answers is essential for accuracy.
Understanding the basics of linear equations and their solution methods is key to successfully solving mathematical problems.

10:54

Verifying Equations: Importance and Practical Examples

The text discusses verifying a mathematical concept through the equation x + 2y = 1.
It emphasizes the importance of questioning and verifying the correctness of concepts.
The text guides on solving equations and checking the correctness of the results.
It involves multiplying values and ensuring the equality of both sides of the equation.
The text explains the process of substitution method in solving equations.
It details the steps of substituting values and finding the correct answers.
The text provides a practical example of substituting values and calculating the final answer.
It highlights the importance of understanding and applying mathematical methods correctly.
The text encourages practicing different methods to solve equations for better understanding.
It concludes by emphasizing the importance of verifying answers and understanding the methods used in solving mathematical problems.

23:20

"Mastering Equations: Methods for Accurate Solutions"

Equations are introduced with various numbers and variables like 5, 1, 6, 8, 68x, 15, 538, and 408.
The process involves adding, dividing, and multiplying these numbers and variables to find values.
The text emphasizes the importance of understanding equations and avoiding mistakes in calculations.
Specific values are derived through equations, such as 4, 28, 404, 102, 75, 60, and -3.
The method of substitution and elimination is explained for solving equations with multiple variables.
Detailed steps are provided for solving equations using the elimination method, focusing on numerical accuracy.
The text highlights the significance of choosing the right method for solving equations with fractions.
Practical examples are given to illustrate the process of solving equations step by step.
The importance of clarity and simplicity in solving mathematical equations is emphasized throughout the text.
The text concludes by encouraging practice and understanding of the methods discussed for solving equations effectively.

35:03

Solving Equations with Elimination Method

The text discusses solving equations using the elimination method.
It emphasizes changing signs when subtracting equations.
The process involves identifying coefficients and changing signs accordingly.
The text explains the steps to solve equations by eliminating variables.
It highlights the importance of multiplying equations to align coefficients.
The text details the process of changing signs and performing subtraction.
It illustrates how to simplify equations by eliminating variables.
The text emphasizes the significance of changing signs during the elimination process.
It outlines the steps to solve equations using the elimination method.
The text concludes by highlighting the importance of understanding and applying the elimination method accurately.

47:43

"Mathematical Puzzle: Solving Equations and Operations"

Start with 3 items, one is removed, leaving 2.
The remaining 2 items are divided by 23, resulting in 207.
One item is moved to the 23rd position and divided by A, yielding 9.
Multiplying the result by 3 gives 27.
Dividing 42 into 3 parts results in 14.
Solving an equation, 3x + 9 = 105, gives x = 32.
Subtracting 3 from 15 leaves 12.
Dividing 42 by 3 gives x = 14.
Solving another equation, 3x - 4y = 4, leads to x = 33.
The final equation, 3x + 3 = a - 2, simplifies to a = 56.

01:01:14

Solving Equations with LCM and Elimination

The text discusses finding the Least Common Multiple (LCM) of two numbers, emphasizing the importance of identifying the common denominator.
It highlights the process of determining the LCM by taking the larger number as the denominator and multiplying both sides by it.
The text explains the steps involved in solving equations with fractions, focusing on changing signs and simplifying expressions.
It mentions the application of the elimination method in solving equations with variables, emphasizing the need to find a common multiple to eliminate terms.
The text provides examples of solving equations using the elimination method, detailing the multiplication of equations by common multiples to simplify and solve the equations.
It underscores the significance of identifying the LCM of numbers to facilitate the elimination method in solving equations.
The text elaborates on the process of multiplying equations by common multiples to align terms and simplify the equations for solving.
It emphasizes the importance of maintaining accuracy in calculations and ensuring that the equations are correctly simplified and solved.
The text encourages the use of the elimination method in solving equations with variables, highlighting the need to find common multiples for effective elimination.
It concludes by reiterating the importance of understanding the elimination method and applying it to solve equations with variables accurately.

01:13:11

"Mathematical Operations and Equations Explained"

The initial numbers are 198, 6, 8, 82116, 2176, and 102.
Multiplication is done by 3, resulting in 306.
The concept of adding and subtracting is introduced.
The idea of mines and forests being cut down is explained.
The calculation of 93 minus 4 is discussed, resulting in 89.
Division is mentioned, with the value of 13 being divided.
The process of finding the value of A is detailed.
Equations involving A and X are solved step by step.
The importance of careful calculations is emphasized.
A complex equation involving fractions and coefficients is explained in detail.

01:25:16

Solving Equations with Fractions: A and B

The first equation involves calculations like 1/6 * 6 = 1, 6 * 2 = 12, and 3 * 2 = 6.
The second equation is introduced, emphasizing the need to solve it.
Multiplication steps are detailed, such as 2 * 3 = 6a and 2 * 2 = 4b.
Subtraction is highlighted, with 6 out of 12 resulting in 6a = 0.
The value of A is determined to be 1/6.
The second equation is presented, with 3 * 6 + 2b = 0 and 3 * 2 = 6.
Further calculations are shown, leading to the value of B being 1/4.
The process of solving 1/x = a and 1/a = b is explained.
The values of A and B are found to be 1/6 and -4, respectively.
The completion of questions 16 and 15B is discussed, focusing on fractions and the subsequent steps.

01:38:49

Solving Equations for X, A, B Values

Brother A received 1/3 of the value of A.
Calculated the value of A and B separately.
Determined the value of X and A.
Solved the question twice to understand the process.
Analyzed the equation 1/X + A = A.
Calculated the value of 1/X + A = A.
Explored the equation 1/X - A = B.
Calculated the value of 1/X - A = B.
Resolved the equations involving A, X, and B.
Concluded the values of X, A, and B through mathematical operations.

01:51:28

"Dividing Mangoes: Equations and Leftovers"

52 mangoes are to be divided between two people.
If 52 mangoes are taken, the remaining amount is x - a.
Dividing by 210852, the value from 2008 is 252.
The cat and dog's value is 4.
Equation number three is derived from 'si' and 'it is from you'.
Subtracting equation one from equation two results in 98.
After subtraction, 6x of the mines are left.
23 mines of 6 plus 29 mines of 6x equal 12 mines.
If six mangoes are taken out, there will be leftovers.
The value of A is -1, obtained through equations three and four.

02:03:44

Solving Equation for Equilateral Triangle Side Length

The value of x in the equation is determined by solving for A, with x being equal to 3 and A being equal to 15, resulting in an equilateral triangle with each side measuring 15 cm.
The exercise involves finding the values of x and A, with the solution leading to the identification of the side length of an equilateral triangle, which is 15 cm for each side.

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