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Important Questions for CBSE Class 10 Maths Chapter 3 - Pair of Linear Equations in Two Variables

Answers to all exercise questions, examples and optional questions have been provided with video of each and every question. We studied Linear Equations in Two Variables in Class 9, we will study pair of linear equations in this chapter. Note: When you click on a link, the first question will open. To open any other question of the exercise, go to the bottom of the page. There is a list with arrows having all the questions with important questions also marked.

On signing up you are confirming that you have read and agree to Terms of Service. Answers to Ch 7 Maths Class 10 Extra Questions Usage all exercise questions, examples and optional questions have been provided with video of each and every question We studied Linear Equations in Two Variables ch 3 maths class 10 extra questions wrong Class 9, we will study pair of linear equations in this chapter.

Serial order wise Ex 3. Forming equations graphically and algebraically. Finding ratios Consistency. Solving equations graphically.

Cross Multiplication Method. Mix questions - Equation given. Mix questions - Equation to be formed. Teachoo is free. Login to view ch 3 maths class 10 extra questions wrong pages. Or login Sign In.

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Expert mathematicians of Vedantu have prepared a set of important questions of chapter 3 Maths class 10, which will help the students revise the chapter easily. The pdf is free for the Ch 10 Maths Class 10 Extra Questions Set students who register for the site. Equations with first order are known as linear equations. The word linear defines the equation is in a line of the coordinate system.

Therefore, any equation lying in a straight line is known as a linear equation. These equations consist of the highest exponent of variables as one and hence, are known as first-degree equations. There are various types of linear equations. When an equation has only one variable or a homogeneous variable, then that type is known as a linear equation with one variable.

In other words, an equation in a line is achieved by relating zero to any field of linear polynomial from which we can obtain the coefficients id known as a linear equation with one variable.

The answers of linear equations produce values that make a true equation when exchanged with unknown values. However, when it comes to two variables linear equation, the Euclidean plane's answer is calculated as Ch 7 Maths Class 10 Extra Questions Vba Cartesian coordinates. A line is determined in an X-Y plane through various forms. Here, we have a list of some common conditions which we use to solve linear equations. Slope Intercept Form. General Form. Intercept Form. Two-point Form.

Point Form. The combination of variables and constants form a linear equation. The most common way to solve linear equations is in the slope-intercept form. Considering the points on the x-y plane, a straight line equation is formed as the linear equation.

The intercept form is represented when the axes of the lines intersect in two different points on the x-y plane and are neither parallel to the y-axis or the x-axis. Suppose x 1 ,y 1 and x 2 ,y 2 are two points, and only one line passes through these points, then the linear equation is represented as.

To solve a linear equation, you must balance both sides of the equation. When you place the equality sign in between the equation, it denotes that the value on both sides of the equation is equal.

The balanced equation requires specific ways of solving it as you cannot change anyone side's value. To find the value of x, the first step is to simplify both sides and then put all the x consonants on one side, finding out the value of x. There are different methods that you can use to solve linear equations with two variables.

Substitution method. Therefore, it has no solution. So, the given pair of lines is inconsistent. Therefore, these lines have infinitely many solutions. Hence, the given pair of linear equations are consistent. We observe that the lines represented by i and ii are coincident. Write the vertices of the triangle formed by these lines and the y-axis.

Also, find the area of this triangle? How many such lines can we find? Therefore, the pair of equations has a unique solution. Hence, these equations are consistent. Find x and y. Question 16 Two years ago, Salim was thrice as old as his daughter and six years later, he will be four years older than twice her age. How old are they now? Now, by first condition, Two years ago, Salim was thrice as old as his daughter.

Question 17 The age of the father is twice the sum of the ages of his two children. After 20 years, his age will be equal to the sum of the ages of his children. Find the age of the father. Solution: Let the present age in year of father and his two children be x, y and z years, respectively. Question 18 Two number are in the ratio 5 : 6, If 8 is subtracted from each of the numbers, the ratio becomes 4 : 5.

Find the numbers. Solution: Let the two numbers be x and y. Question 19 There are some students in the two examination halls A and B. To make the number of students equal in each hall, 10 students are sent from A to 8. But if 20 students are sent from B to A, the number of students in A becomes double the number of students in B. Find the number of students in the two halls. Solution: Let the number of students in halls A and B are x and y respectively.

Question 20 A shopkeeper gives books on rent for reading. She takes a fixed charge for the first two days, and an additional charge for each day thereafter. Find the fixed charges and the charge for each extra day. Jayanti answered questions and got 90 marks. How many questions did she answer correctly? Solution: Let the number of correct answers be x then the number of wrong answers be � x Then, by given condition, Hence, Jayanti answered correctly questions.

Find x and y and hence the values of the four angles. Also find the area of the quadrilateral formed by the lines and the x-axis. Now, from the graph ABCD is the quadrilateral formed by given lines and x � axis. Form the pair of linear equations for the above situation.

Find the cost of a pen and a pencil box. On solving lines i and ii , we will get the intersecting point B On multiplying eq. On solving lines iii and i , we will get the intersecting point A On multiplying in eq.

Question 6 Ankita travels 14 km to her home partly by rickshaw and partly by bus. She takes half an hour, if she travels 2 km by rickshaw, and the remaining distance by bus. On the other hand, if she travels 4 km by rickshaw and the remaining distance by bus, she takes 9 minutes longer.

Find the speed of the rickshaw and of the bus. Now, time taken to travel 2 km by rickshaw, and time taken to travel remaining distance i. Find the speed of the stream. Question 8 A motorboat can travel 30 km upstream and 28 km downstream in 7 hours. It can travel 21 km upstream and return in 5 hours. Find the speed of the boat in still water and the speed of the stream.

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