DELHI PUBLIC SCHOOL, JANKIPURAM,LUCKNOW
Class X (MATHEMATICS) 2020-21
QUESTION BANK: Chapter 3(Linear Equations in 2 variables)
“Mathematics is not about numbers, equations, computations or algorithm: it is all about understanding.”
William Paul Thurston
1) Write a pair of linear equations which has a unique solution x=2 , y= -1.How many such pairs
can you write?
2) Solve the following pair of equations 5x+4/y = 9, 7x- 2/y =5 and hence find the value of k in
y = kx + 1.
3) If x/3 + y/4 = 6 and x/6 + y/2 =6, find the values of x/y +1/2.
4) Solve the following pair of equations 55x +67y = 311
67x + 55y = 299.
5) Draw the graph of the equations 2x +3 y = 6, and 4x + 6y = 12. Determine the area formed
by these lines and the coordinates axis and shade the region.
6) Solve for x and y : 2x + 3y = 17 and 2 x + 2 – 3 y+1 = 5
7) Determine graphically the vertices of a trapezium , the equations of whose sides are
x= 0 , y = 0 , y = 4 and 2x + y = 6 . Also, determine its area.
8) Find the value of p and q for which the following system of linear equations has infinite
number of solutions.
2x + 3y = 7
(p + q)x + (2p –q )y = 3 ( p+q + 1)
9) Two rails are represented by the equations
x + 2y – 4 = 0 and 2x + 4y – 12 = 0. Will the rails cross each other?
10) 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.
11) 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?
12) For which values of p does the pair of equations given below has unique solution?
4x + py + 8 = 0
2x + 2y + 2 = 0
13) 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
14) A boat goes 30 km upstream and 44 km downstream in 10 hours. In 13 hours, it can go 40 km
upstream and 55 km down-stream. Determine the speed of the stream and that of the boat in
still water.