Concise Mathematics Class 8 ICSE Solutions for Chapter 14 - Linear Equations in One Variable
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To calculate the unknown quantity with the brief information given in any question, a stronghold on the important concepts of algebraic expressions is important. This chapter covers an introduction and two exercises that deal with the linear equations in one variable. The number of questions included in exercise 4(a) and 4(b) are 12 and 32 respectively.
The Selina textbook chapter 14 is the continuation of the concepts of algebraic expressions that students must have studied in their previous classes. In this chapter, students will learn to solve equations in one variable. Some important topics covered in this chapter are as follows.
An algebraic equation is an equation involving variables. It states that in an equation, the value of the expression given on the left-hand side is equal to the value of the expression given on the right-hand side.
Similar to the numbers, the variables can also be shifted from one side of the equation to the other.
There may be algebraic expressions on both sides of an equation.
This chapter consists of problems on numbers, ages, a combination of currency notes and coins, etc.
In general, algebraic expressions are simplified in the same way we simply numeric expressions. Some equations may not be linear but they can be brought to the linear form by multiplying both sides of the equation with a suitable expression.
The linear equations are the equations of the first order. These equations represent various lines in the coordinate system. Linear equations are also known as first-degree equations as the highest exponent of variables is 1, in any linear equation. Examples of linear equations are:
4p - 3 = 0
p + 1= 0
p + q = 2
The equations that consist of only one type of variable are known as linear equations in one variable. The linear equations in one variable are expressed in the form of px + q = 0, where ‘p’ and ‘q’ are two integers, x is an unknown variable. It has only one solution. For example, 2p + 3 = 8 is a linear equation having only one variable in it. Hence, this equation has only one solution i.e. p = 5/2. The linear equations in two variables have two solutions.
A linear equation in one variable is an equation that consists of a maximum of one variable of order 1. The representation of a linear equation is in the form of px + q = 0, where x is an unknown variable. There is only one solution to a linear equation. Some more examples of linear equations in one variable are:
5p = 1
11p -1 = 0
5p + 3 = 6
The standard form of linear equation in one variable is given as:
px + q = 0
‘P’ and ‘q’ are real numbers
Both ‘p’ and ‘q’ are not equal to zero.
Following are the steps to solve linear equations in one variable:
Simplify each side of the equation, if required.
Use arithmetic operators to move the variable terms to one side and the constant terms to another side of the equation.
Make use of the multiplication/division operations to discard the coefficients of the variables.
Check if your answer satisfies the equation.
Students can refer to Vedantu's ICSE Selina Solutions PDF to get assistance for solving ICSE Selina textbook sums. Also, they can verify the solutions prepared by them by comparing them with these solutions. These Selina ICSE solutions for class 8 chapter 14 are explained in simple stepwise methods.
The solution to every sum is explained in an easy to understand manner, emphasizing the basic principles, formulas, rules, and applications of linear equations.
These solutions are prepared by the subject matter experts at Vedantu in a stepwise manner. The step by step method followed in the solutions helps students to understand the appropriate problem-solving approaches.
For certain sums, alternative methods of solutions are provided, so that students can practice the method that suits there convenience.
It saves the students a lot of time before the exams, as all the important concepts of linear equations in one variable are highlighted in these solutions.
The Vedantu ICSE Selina Solutions are available in the PDF format. The students can download this PDF for free to study offline and can also refer to these study materials online. The PDF files for every chapter of the Selina Maths book are provided here separately and can be downloaded from the links given on this page. The Selina textbook for Maths is prescribed for the ICSE students. The concepts and theories are explained in this book in a simple and logical manner. The sums for every topic are grouped under separate exercises, which makes it easier for the students to practice any topic at a time. By following the Selina Solutions students will be able to understand the problem-solving techniques thoroughly.
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