Exercise 3.3: Substitution Method

The cost of 5 pens and 7 notebooks is ₹255, while the cost of 7 pens and 5 notebooks is ₹249. What is the cost of one pen and one notebook, respectively?

The sum of the digits of a two-digit number is 9. Also, nine times this number is twice the number obtained by reversing the order of the digits. Find the number.

If 1/(x+y) + 1/(x-y) = 3 and 3/(x+y) - 2/(x-y) = 4, what is the value of x^2 - y^2?

If x and y are two numbers such that their sum is 8 and twice the first number minus the second number is 7, which pair of linear equations represents this?

For what values of 'k' will the following pair of linear equations have infinitely many solutions? kx + 3y - (k - 3) = 0 12x + ky - k = 0

A man travels 600 km partly by train and partly by car. If he covers 400 km by train and the rest by car, it takes him 6 hours and 30 minutes. But if he travels 200 km by train and the rest by car, he takes 7 hours. Find the speed of the train.

Find the value of 'm' for which the pair of linear equations mx + y = 1 and (m² + 1)x + (m - 1)y = m has no solution.

Consider the system of linear equations a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0. Which of the following statements must be true if a1b2 - a2b1 = 0 and b1c2 - b2c1 = 0?

A boat covers 30 km upstream and 44 km downstream in 10 hours. In 13 hours, it can cover 40 km upstream and 55 km downstream. Determine the speed of the stream.

Five years ago, Nuri was thrice as old as Sonu. Ten years later, Nuri will be twice as old as Sonu. Let Nuri's present age be 'x' years and Sonu's present age be 'y' years. Which pair of linear equations correctly represents this situation?