Linear equation in two variables Previous year question paper class 10.

Q1). Formulate the following problems as a pair of equations, and hence find their solutions:

Anjan can row downstream 40 km in 4 hours, and upstream 2 km in 1 hours. Find her speed of rowing in still water and the speed of the current.

Q2). Solve the following pair of linear equations:

y -4x= 1
6x- 5y= 9

Q3.) Solve using cross multiplication method:

x+y=1

2x – 3y = 11.

Q4). Solve for x and y

x + 2y – 3= 0
3x – 2y + 7 = 0

Q5). Solve for x and y,

2x= 5y + 4;

3x-2y + 16 = 0

Q6). 6(ax + by) = 3a + 2b

6(bx – ay) = 3b -2a

Find the value of x and y.

Q7). If the system of equations

6x + 2y = 3 and kx + y = 2 has a unique solution, find the value of k.(CBSE 2013)

Q8). How many solutions does the pair of equations y = 0 and y = -5 have? (2013)

Q9). For what value of k, the pair of equations 4x – 3y = 9, 2x + ky = 11 has no solution? (2017D)

Q10). Calculate the area bounded by the line x + y = 10 and both the co-ordinate axes. (2012)

Q11). Find whether the following pair of linear equations is consistent or inconsistent: (2015)

3x + 2y = 8 6x – 4y = 9

Q12). Draw the graph of

2y = 4x – 6; 2x = y + 3 and determine whether this system of linear equations has a unique solution or not.

Q13). Draw the graph of

2y = 4x – 6; 2x = y + 3 and determine whether this system of linear equations has a unique solution or not.

Q14). Represent the following pair of equations graphically and write the coordinates of points where the lines intersect y-axis.

Q15). Solve the following pair of linear equations for x and y:

141x + 93y = 189;

93x + 141y = 45 (2013)

Q16).Solve by elimination: (2014)

3x = y + 5

5x – y = 11

Q17). Solve by elimination: 2015

3x – y – 7

2x + 5y + 1 = 0

Solve the following pair of equations: (2014)

49x + 51y = 499

51x + 49 y = 501

Q18). Find the two numbers whose sum is 75 and difference is 15. (2014)

Q19). Solve the following pair of linear equations by the cross multiplication method: x + 2y = 2; x – 3y = 7 (2015)

Q20). Srikant earns ₹600 per month more than his wife. One-tenth of the Srikant's salary and l/6th of the wife’s salary amount to ₹1,500, which is saved every month. Find their incomes. (2014)

Q21). The sum of the digits of a two digit number is 8 and the difference between the number and that formed by reversing the digits is 18. Find the number. (2015)

Q22). The age of the father is twice the sum of the ages of his 2 children. After 20 years, his age will be equal to the sum of the ages of his children. Find the age of the father. (2012)