## The ages of two friends Ani and Biju differ by 3 years. Ani’s father Dharam is twice as old as Ani and Biju is twice as old as his sister Cathy. The age of Cathy and Dharam are differ by 30 years. Find the ages of Ani and Biju.

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 …

## Formulate the following problem as a pair of equations, and hence find their solutions

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 …

## Solve the following pairs of equations by reducing them to a pair of linear of linear equations

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    $$4\over \sqrt{x}$$ – $$9\over \sqrt{y}$$ …

## From the pair of linear equations in the following problem and find their solutions (if they exist) by any algebraic method :

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 …

## Solve the following pair of linear equations by the substitution and cross-multiplication methods : 8x + 5y = 9 and 3x + 2y = 4

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 …

## For what values of a and b, the following system of equations have infinite number of solutions ?

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 …

## 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.

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 …

## From the pair of linear equation in the following problems, and find their solutions (if they exist) by the elimination method

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. …

## Solve the following pair of linear equations by the elimination method and the substitution method

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 + …

## Form the pair of linear equations for the following problems and find their solution by substitution method.

Question :  Form the pair of linear equations for the following problems and find their solution by substitution method. (i)  The difference between two numbers is 26 and one number is three times the other. Find them. (ii)  The larger of two supplementary angles exceeds the smaller by 18 degrees. Find them. (iii)  The coach …