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RS Aggarwal Solutions Class 10 Chapter 3 - Linear Equations in two variables (Ex 3E) Exercise 3.5

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Last updated date: 22nd Mar 2024
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Download Free PDf of RS Aggarwal Solutions Class 10 Chapter 3 - Linear Equations in Two Variables (Ex 3E) Exercise 3.5 Available on Vedantu

Free PDF download of RS Aggarwal Solutions Class 10 Chapter 3 - Linear Equations in two variables (Ex 3E) Exercise 3.5 solved by Expert Mathematics Teachers on Vedantu.com. All Ex 3.5 Questions with Solutions for Class 10 Maths RS Aggarwal to help you to revise the complete Syllabus and Score More marks. Register for online coaching for IIT JEE (Mains & Advanced) and other engineering entrance exams. You can also Download NCERT Maths NCERT Solutions Class 10 to help you to revise the complete Syllabus and score more marks in your examinations. Vedantu is a platform that also provides free NCERT Solution and other study materials for students. Subjects like Science, Maths, English will become easy to study if you have access to NCERT Solution for Class 10 Science, Maths solutions, and solutions of other subjects that are available on Vedantu only.

Competitive Exams after 12th Science

Chapter 3 of Class 10, that is, Linear Equations in Two Variables - At A Glance

  • The two Linear Equations having the same two variables are known as a pair of Linear Equations in two variables.

  • A pair of Linear Equations can be represented in a graphical or algebraic method.

  • Three algebraic methods can be used to find the solution of a pair of Linear Equations: substitution method, elimination method and cross-multiplication method.

  • A pair of Linear Equations can be consistent, inconsistent or it may be dependent and consistent.

  • There can also be lines that are represented by two equations but are not linear.

How to Plot a Straight Line?

Graphs make result interpretation and representation an easy task. Plotting a straight line on a graph is an easy task if students follow the following steps:

  • For plotting the value of a variable on the graph, we must have a known and an unknown value. Therefore, we will take any value for one of the variables, say x1, and substitute that value in the equation to get the corresponding value of the other variable.

  • Now, put any value of y to get the corresponding value of x. This will give you two pairs of values for the variables.

  • Plot these two points on the graph and draw a line through these points.

What is the Nature of Two Straight Lines in a Plane?

The two straight lines in a plane have three possibilities

  1. The two straight lines intersect at exactly one point in a plane.

  2. The two straight lines can be parallel to each other, that is, they don’t intersect at any point in a plane.

  3. The two straight lines in a plane can be coincident.

FAQs on RS Aggarwal Solutions Class 10 Chapter 3 - Linear Equations in two variables (Ex 3E) Exercise 3.5

1. When can an equation be considered as a Linear Equation of Two Variables?

According to Class 10 Chapter 3, that is, Linear Equations in Two Variables, a simple equation is said to be a linear equation of two variables when it is possible to present the equation in the form of ax+by+c=0. In the given equation, a,b, and c are either constants or real numbers. The value of a and b should not be equal to 0. In this equation, a, b and c are real numbers and x and y are the two unknown variables. For instance, 4x+5y+3=12 will be considered as a linear equation of two variables. 

2. How can I interpret the Linear Equation of Two Variables of Class 10 Chapter 3?

Interpreting the results of Linear Equations of two variables of Class 10 Chapter 3 is a very simple process. Suppose, you have the following equation 4x + 5y +3 = 12. In this equation, the two unknown variables are x and y. The coefficients of x and y are real numbers, that is, 4 and 5 respectively. Therefore, after solving the equation, we will get one value for x and y each, which will make the two sides of the linear equation equal.

3. How can I solve the Class 10 Chapter 3 linear equation of two variables?

As per Class 10 Chapter 3, Linear Equations in Two Variables, the solution of the linear equation of two variables, such as ax+by=c, will be represented by a specific point on the graph paper. In this case, to get the first value we will multiply the x coordinate by a, and to find the second value, students must multiply the y coordinate by b and the sum of these the value of a and b will be equal to c. Thus, there is a possibility of an infinite number of values and solutions in the case of Linear Equations with two variables.

4. Why is it beneficial to solve Class 10 Chapter 3 Linear Equations with two variables graphically?

There are many ways for solving Linear Equations with two variables. Still, plotting a graph is one of the easiest and most accurate methods of representation of data. It also provides an important way for the visual representation of the equations which can help students understand the concept better. To solve Linear Equations with two variables in the form of a graph, we should identify two separate equations, each having two variables. Therefore, students should identify two separate line equations and then represent them on a graph.

5. What are tips that I should follow for attempting RS Aggarwal Solutions for Chapter 3 Class 10, exercise 3.5?

Exercise 3.5 of Chapter 3, that is, Linear Equations with two variables deal with certain conceptual questions. To solve questions in this exercise, students must remember the condition for the pair of Linear Equations to have infinite solutions or no solution. In the case of infinite solutions rule out the values which do not satisfy all the ratios. Also, study cross multiplication method also as questions from this section are asked.