Solution : Let two friends named as P and Q. Let P has Rs x and Q has Rs y. According to Question, x + 100 = 2(y – 100) \(\implies\) x – 2y + 300 = 0 ………(1) y + 10 = 6(x – 10) \(\implies\) 6x – y – …
Solution : Let x and y be the ages of Ani and Biju respectively. Then, According to Question, x + y = \(\pm 3\) Dharam’s age = 2x, and Cathy’s age = \(y\over 2\) Clearly, Dharam is older than Cathy. So, 2x – \(y\over 2\) = 30 \(\implies\) 4x – y = 60 Thus, we …
Question : Formulate the following problem as a pair of equations, and hence find their solutions (i) Ritu can row downstream 20 km in 2 hours, and upstream 4 km in 2 hours, find her speed of rowing in still water and the speed of the current. (ii) 2 women and 5 men can together …
Formulate the following problem as a pair of equations, and hence find their solutions Read More »
Question : Solve the following pairs of equations by reducing them to a pair of linear of linear equations : (i) \(1\over 2x\) + \(1\over 3y\) = 2 and \(1\over 3x\) + \(1\over 2y\) = 2 (ii) \(2\over \sqrt{x}\) + \(3\over \sqrt{y}\) = 2 and \(4\over \sqrt{x}\) – \(9\over \sqrt{y}\) …
Question : From the pair of linear equations in the following problem and find their solutions (if they exist) by any algebraic method : (i) A part of monthly hostel charges is fixed and the remaining depends on the number of days one has taken food in the mess. When a student, A takes food …
Solution : The given linear equations are : 8x + 5y = 9 ………..(1) 3x + 2y = 4 ………..(2) By Substitution Method : Form equation (1), y = \(9 – 8x\over 5\) Substitute the value of y in equation (2), we get …
Question : (i) For what values of a and b, the following system of equations have infinite number of solutions ? 2x + 3y = 7 (a – b)x + (a + b)y = 3a + b – 2 (ii) For what value of k will the following pair of linear equations have no solution …
Question : Which of the following pairs of linear equations has unique solutions, no solution, or infinitely solution ? In case there is a unique solution, find it by using cross multiplication method. (i) x – 3y – 3 = 0 and 3x – 9y – 2 = 0 (ii) 2x …
Question : From the pair of linear equation in the following problems, and find their solutions (if they exist) by the elimination method : (i) If we add 1 to the numerator and subtract 1 from the denominator, a fraction reduces to 1. It becomes \(1\over 2\) if we only add 1 to the denominator. …
Question : Solve the following pair of linear equations by the elimination method and the substitution method : (i) x + y = 5 and 2x – 3y = 4 (ii) 3x + 4y = 10 and 2x – 2y = 2 (iii) 3x – 5y – 4 = 0 and 9x = 2y + …
