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Learn to understand a real-life situation mathematically. The concept insights in our NCERT textbook solutions will help you represent linear equations graphically or algebraically. To understand linear equations, you should also explore our Maths topic notes, concept videos and other resources.

Concept insight: Cost of bats and balls needs to be found so the cost of a ball and bat will be taken as the variables. Applying the conditions of total cost of bats and balls algebraic equations will be obtained. Then, in order to represent the obtained equations graphically take atleast three ordered pairs on both the equations in order to avoid any computational errors.

Concept insight: In order to answer such questions, remember the condition for the pair of linear equations to be intersecting, parallel or coincident. Also, while writing the coefficients, don't forget to ncert solutions for class 10 maths ch 3 study rankers war the signs.

For elimination, we multiply one nncert or sometimes even both equations by suitable constant to make the coefficient of one variable same in sklutions the equations.

The trick is to eliminate that variable which involves lesser computations. In order to solve the given pair of equations by substitution method, we need to substitute the value of any one of the variable from any one of the equation. The trick here is to make sure you substitute the value of that variable which simplifies your calculations. Note that the solution must be same in both the cases.

The numerator and denominator of the fraction are not known so we represent these as variables x and y respectively where variable y must be non zero.

Then, a pair of linear equations can be formed from the given conditions. The pair of equations can ncert solutions for class 10 maths ch 3 study rankers war be solved by eliminating a suitable variable. Concept insight: Here, Nuri's and Sonu's present age are not known.

So, we will write both these in terms of variables. Then, using the given conditions, a pair of linear equations can be formed. Then, using the two given conditions, a pair of linear equations sutdy be formed which can be solved by eliminating one of the variables. Concept insight: This problem talks about two types of notes, Rs 50 notes and Rs notes. And the number of both these notes with Meena is not known. So, we denote the number of Rs 50 notes and Rs notes by variables x and y respectively.

Now two linear equations can be formed by the given conditions which can be solved by eliminating one of the variables. Ncert solutions for class 10 maths ch 3 study rankers war insight: Here, the fixed charges for the first sttudy days and per day charges are not known so, they will be represented using two different variables.

The two equations can then be obtained ncert solutions for class 10 maths ch 3 study rankers war using the given conditions which can be solved by eliminating one of the variables. Thus, the given pair of equations has no solution. Thus, the given pair of equations has unique solution. By cross-multiplication method, Thus, the given pair of equations has infinite solutions.

The solutions can be obtained by assuming the value of solutlons to be kwhere k is any. So, the ordered pairsflr k is a constant, are the solutions of. By cross-multiplication, Concept Insight: In order to answer such questions, remember the condition for the pair of linear equations to have unique, infinitely many or no solution relating the coefficients.

Also, remember the formula used to solve by cross multiplication method. While applying the formula, be careful about the signs of the coefficients. Concept insight: Here, the fixed matns of the food and charge for food per day are the unknown quantities.

So they are taken as variables x and y. The two equations can then be obtained by using the given conditions. You will observe that the variable x has the same coefficient in both the equations, so it will be easier to find the solution by eliminating x from both the equations. Also, one can solve the system by other methods. The numerator and denominator of the fraction need to be represented by variables. A pair of linear equations can be obtained from the given conditions.

Observe that the variable y has the same coefficient in both the equations, so it will be easier to find the solution by eliminating y from both the equations. Therefore, the total number of questions in the test is Concept insight: In this problem, the number of right answers and the number c,ass wrong answers answered by Yash are the unknown quantities.

So, they must be represented by two variables. A pair of linear equations can be obtained by applying the given condition.

Variable y has the same coefficient in both the equations, so it will be easier to find the solution by eliminating y from both the equations. Concept insight: In this problem, the speeds of the flass cars are not known so we will represent them by variables. Remember that when the cars are travel in the same direction, then the speed will be equal to the difference of their speeds and when they studh in opposite direction, then the speed will be equal to the sum of their speeds.

Don't miss to write the unit. Thus, the length and breadth of the rectangle are 17 units and 9 units respectively. Concept insight: Here, the length and the silutions of the rectangle will be represented by variables. Then, the pair of equations will be written from the given conditions. Solution can be easily computed using the cross multiplication method. Concept insight: Two unknown quantities are speed in still water and the speed of the current, which can be represented by variables x and y respectively.

Ncertt using the given conditions, two linear equations can be formed. Now, the two equations can be solved easily by the substitution method. Concept insight: In this problem it is mentioned that a girl Roohi travels to her home partly by train and partly by oslutions. So, we represent the speed of the train and bus ncert solutions for class 10 maths ch 3 study rankers war variables u and v respectively. Here, to answer this problem, remember the fact that speed is the ratio of distance and time.

Using this and the given conditions, formulate pair of linear equations. Observe that the equations obtained are ncert solutions for class 10 maths ch 3 study rankers war linear.

So, first step will be to convert them into linear form by suitable substitution and then sstudy it using an appropriate algebraic method. Let the number of rows be x and number of students in a row be y. So, in order to know the total number of ncert solutions for class 10 maths ch 3 study rankers war, it is must to know the number of students standing in each row and the total number of rows.

So, these two quantities are represented by variables x and y. Use the mathx given in the question to obtain a pair of equations. The pair of equations can then be solved easily by eliminating a suitable variable. Enter the OTP sent to your number Change. Resend OTP. Starting early can help you score better! Avail Offer. Ok Cancel. Ok Choose Chapter. Ok Choose Topic.

Yes No. Choose Subjects. Choose Chapters. Let the present age of Aftab and his daughter be x and y respectively. Here, Aftab and his daughter's present age needs to be found so, so the ages will be represented by variables x and y. The problem talks about their ages seven years ago and three years from. Here, the words 'seven years ago' means we have to subtract 7 from their present ages, and 'three years from now' or 'three years hence' means we have to add 3 to their present ages.

Remember in order to represent the algebraic equations graphically the solution set of equations must be taken as whole numbers only for the accuracy.

Graph of the two linear equations will be represented by a straight line. Let the cost of a bat and a ball be Rs x and Rs y respectively. Let the cost of 1 kg of apples and 1 kg grapes be Rs. The given condtions can be algebraically represented as: Three solutions of this equation can be written in a table as follows: x 50 60 70 y 60 40 20 Three solutions of this equation can be written in a table as follows: x 70 80 75 y 10 0 The graphical representation is as follows: Concept insight: cost of apples and grapes needs to be found so the cost of 1 kg apples and 1 kg grapes will be taken as the variables.

From ncert solutions for class 10 maths ch 3 study rankers war given conditions of collective cost of apples and grapes, a pair of linear equations in two variables will be obtained. Then, in order to represent the obtained equations graphically, take the values of variables as whole numbers.

Thus, the number of girls and boys in the class are 7 and 3 respectively. Therefore, the cost of one pencil and one pen are Rs 3 and Rs 5 respectively. Concept insight: Read the question carefully and examine what are the unknowns. Represent the given conditions with fo help of equations by taking the unknowns quantities as variables.

Also carefully state the variables as whole solution is based on it. On the graph paper, mark the points accurately and neatly using a sharp pencil. Also, take at least three points satisfying the two equations in order to obtain the correct straight line of the equation.

Since joining any two points gives a straight line and if one of the points is computed incorrect will give a wrong line and taking third point will give a correct line. The point where the two straight lines will intersect will give the values of the two variables, i. State the solution point.

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