RS Aggarwal Chapter 3 Class 10 Maths Exercise 3.6 (ex 3f) Solutions

RS Aggarwal Chapter 3 Class 10 Maths Exercise 3.6 Solutions: The solutions of RS Agarwal for Class 10, Chapter 3, are ready to help you understand the graph of linear equations. In this chapter of RS Aggarwal Class 10 Maths Solutions, you will solve linear equations simultaneously in two variables and then create a graph for the equations. You will learn about algebraic methods of solving cross-multiplication, elimination, and substitution of equations. You will identify coherent systems of equations and show how the equation system has unique solutions.

In Exercise 3F you must identify whether the system of equations has a unique solution or no solution or an infinite solution.

Download RS Aggarwal Chapter 3 Class 10 Maths Exercise 3.6 Solutions

 

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Important Definition for RS Aggarwal Chapter 3 Class 10 Maths Ex 3f Solutions

Equation Having a Unique Solution

Suppose we are considering two linear equations:

Equation 1: a1x + b1y + c1 = 0

Equation 2: a2x + b2y + c2 = 0

• A system of equations is said to be having unique solutions when a1/a2≠ b1/b2      
• Let say for an example 1x +2y= 3 and 4x+5y=6,
• So, for a given equation, a1=1, b1=2 and a2=4, b2=5 and c1=3, c2=6
• Here, a1/a2 ≠ b1/b2 so, the system has unique solutions.                                                                                                                                   

Equation Having an Infinite Solution 

A system of equations is said to be having infinite solutions when a1/a2 = b1/b2

Equation having No Solution

When a system of equations has a1/a2 = b1/b2 ≠ c1/c2, the equations are said to be having no solution.

Example of Linear Equation in Two Variables

If an equation is written in the form ax + by + c=0, where a, b, and c are real integers and the coefficients of x and y, i.e. a and b, are not equal to zero, it is said to be a linear equation in two variables.
x+4y = 12 and -x+3y = 2 are two-variable Linear Equations, respectively.

The solution to such an equation is a pair of numbers, one for x and one for y, which equalizes the two sides of the equation.

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