Linear Equations


Find the value(s) of k for which the pair of linear equations kx + y = k2 and x + ky = 1 have infinitely many solutions.


For what values of m and n the following system of linear equations has infinitely many solutions.
3x + 4y = 12
(m + n)x + 2(m – n)y = 5m – 1


In Figure, ABCD is a rectangle. Find the values of x and y.


The sum of a two-digit number and the number obtained by reversing the digits is 66. If the digits of the number differ by 2, find the number. How many such numbers are there?


The ratio of incomes of two persons is 9:7 and the ratio of their expenditures is 4:3. If each of them manages to save Rs. 2000 per month, find their monthly incomes.