Linear Equations (C10)

Pair of linear equations in two variables and graphical method of their solution, consistency/inconsistency. Algebraic conditions for number of solutions. Solution of a pair of linear equations in two variables algebraically - by substitution, by elimination

Find the value of k so that the pair of equations x + 2y = 5 and 3x + ky + 15 = 0

Find the value(s) of k so that the pair of equations x + 2y = 5 and 3x + ky + 15 = 0 has a unique solution.

The larger of two supplementary angles exceeds the smaller

The larger of two supplementary angles exceeds the smaller by 18°. Find the angles.

Sumit is 3 times as old as his son. Five years later

Sumit is 3 times as old as his son. Five years later, he shall be two and a half times as old as his son. How old is Sumit at present ?

Find the value(s) of k for which the pair of linear equations kx + y = k^2 and x + ky = 1

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

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

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

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

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.