Title Pair of Linear Equations in Two Variables .pdf ✅

Previous Years’ Board Questions 1 Mark Questions 1. Write whether the following pair of linear equations is consistent or not.x + y = 14, x − y = 4 [CBSE2009] 2. Find the number of solutions of the following pair of linear equations:x + 2y − 8 = 02x + 4y = 16 [CBSE 2009] 2 Marks Questions 3. Given the linear equation 3x − 4y − 7 = 0, write another linear equation in these two variables such that the geometrical representation of the pair so formed is: (i) intersecting lines(ii) parallel lines [CBSE 2016] 4. For what value of k does the pair of equations given below has a unique solution?y − x = 63 kx + 2y = 7 [CBSE 2016] 5. If the system of equations 6x + 2y = 3 and kx + y = 2 has a unique solution, find the value ofk. [CBSE 2013] 6. Find whether the following pair of linear equations is consistent or inconsistent.3x + 2y = 86x − 4y = 9 [CBSE 2016] 7. Find whether the lines representing the following pair of linear equations intersect at a point, are parallel or coincident:2x − 3y + 6 = 0,4x − 5y + 2 = 0[CBSE 2015] 8. For what value of’k’ the system of equation kx + 3y = 1,12x + ky = 2 has no solution.[CBSE 2011] 9. For what value of k, the pair of linear equations kx − 4y = 3,6x − 12y = 9 has an infinite number of solutions?[CBSE 2012] 10.Solve: 99x + 101y = 499101x + 99y = 501 [CBSE 2011] 3 Marks Questions 11.Find the value of k for which the following pair of equations has no solution:x + 2y = 3, (k − 1)x + (k + 1)y = (k + 2)[CBSE 2011] 12.Find the values of a and β for which the following pair of linear equation has infnite number of solutions:2x + 3y = 7; 2αx + (α + β)y = 28[CBSE 2011] 13.Determine the values of m and n so that the following system of linear equations have infnite number of solutions:(2m − 1)x + 3y − 5 = 03x + (n − 1)y − 2 = 0[CBSE 2013, 11] 14.Solve by substitution:x − y = 23x + 2y = 16 [CBSE 2016] 15.Solve for x and y:2x = 5y + 4; 3x − 2y + 16 = 0[CBSE 2014] 16.Solve for x and y:6 (9x + 6y) = 3a + 2b; 6(bx − ay) = 3b − 2a[CBSE 2014] 17.Solve using cross multiplication method:x + y = 72x − 3y = 11 [CBSE 2016] 18.Solve the following pair of equations: 10 x+y + 2 x−y = 4; 15 x+y − 5 x−y = −2[CBSE 2009] 19.For what values of p and q, will the following pair of linear equations has infnitely many solutions?4x + 5y = 2;(2p + 7q)x + (p + 8q)y = 2q − p + 1[CBSE 2013]
20.Solve for x and y: 5 x−1 + 1 y−2 = 2 and 6 x−1 − 3 y−2 = 1[x ≠ 1, y ≠ 2] [CBSE 2014] 21.Solve the following pair of equations:4 x + 3y = 8; 6 x − 4y = −5 [CBSE 2010] 22.Solve for x and y:ax + by = a+b 2 3x + 5y = 5 [CBSE 2011] 23.Sum of ages of a father and the son is 40 years. If father’s age is three times that of his son, then find their respective ages.[CBSE 2015] 24.A number consists of two digits. When the number is divided by the sum of its digits the quotient is 7. If 27 is subtracted from the number the digits interchange their places, find the number. [CBSE 2010] 25.The sum of the digits of a two digit number is 12. The number obtained by interchanging the two digits exceeds the given number by 18. Find the number.[CBSE 2011] 26.Determine graphically whether the following pair of linear equations 2x − 3y = 5; 3x + 4y = −1 has(i) a unique solution(ii) infinitely many solutions or(iii) no solution [CBSE 2014] 27. 8 men and 12 boys can finish a piece of work in 10 days, while 6 men and 8 boys can finish it in 14 days. Find the time taken by one man alone and that by one boy alone to finish the work. [CBSE 2013] 28. 2men and 7boys can do a piece of work in 4 days. It is done by 4 men and 4 boys in 3 days. How long would it take for one man or one boy to it? [CBSE 2013] 4 Marks Questions 29.The area of a rectangle gets reduced by 9 square units, if its length is reduced by 5 units and the breadth is increased by 3 units. The area is increased by 67 square units if length is increased by 3 units and breadth is increased by 2 units. Find the perimeter of the rectangle. [CBSE 2012] 30.A boat covers 32 km upstream and 36km downstream in 7 hours. Also it covers 40km upstream and 48 km downstream in 9 hours. Find the speed of the boat in still water and that of the stream.[CBSE 2012] 31.A boat takes 4 hours to go 44 km downstream and it can go 20 km upstream in the same time. Find the speed of the stream and that of the boat in still water.[CBSE 2014] 32.Draw the graph of the following equations:x + y = 5; x − y = 5(i) Find the solution of the equations from the graph.(ii) Shade the triangular region formed by the lines and the y‐axis.[CBSE 2012] 33.Solve graphically the pair of linear equations3x − 4y + 3 = 0 and 3x + 4y − 21 = 0Find the co‐ordinates of the vertices of the triangular region formed by these lines
and x‐axis. Also calculate the area of this triangle. [CBSE 2015] 34.Solve the following pair of equations graphically: 2x + 3y = 12, x − y − 1 = 0Shade the region between the two lines represented by the above equation andthe x‐axis. [CBSE 2012] 35.A two digit number is obtained by either multiplying the sum of digits by 8 and then subtracting 5 or by multiplying the difference of digits by 16 and adding 3. Find the number. [CBSE 2012] 36.The area of a rectangle reduces by 160 m2 if its length is increased by 5 m and breadth is reduced by 4 m. However if length is decreased by 10 m and breadth is increased by 2 m, then its area is decreased by 100 m2 . Find the dimensions of the rectangle. [CBSE 2014] 37.A and B are two points 150 km apart on a highway. Two cars start from A and B at the same time. If they move in the same direction they meet in 15 hours. But if they move in the opposite directions, they meet in 1 hour. Find their speeds. [CBSE 2012] 38.Places A and B are 80 km apart from each other on a highway. A car starts from A and another from B at the same time. If they move in the same direction they meet in 8 hours and if they move in opposite directions they meet in 1 hour 20 minutes. Find speeds of the car. [CBSE 2013] 39.A man travels 600 km partly by train and partly by car. It takes 8 hours and 40 minutes if he travels 320 km by train and the rest by car. It would take 30 minutes more if he travels 200 km by train and rest by car. Find the speed of the train and the car separately. [CBSE 2011] 40. 4 chairs and 3 tables cost ¥2100 and 5 chairs and 2 tables cost ¥ 1750, find the cost of one chair and one table separately.[CBSE 2015] 41.The ratio of income of two persons is 11: 7 and the ratio of their expenditures is 9: 5. If each of them managers to save ¥400 per month, find their monthly incomes.[CBSE 2012] 42.Solve the following pair of equations: 2 √x + 3 √y = 2 and 4 √x − 9 √y = −1[CBSE 2015] 43.A man started his job with a certain monthly salary and earned a fixed increment every year. His salary was 15,000 after 5 years service and 19,000 after 10 years service. What was his starting salary and his annual increment? Which charact er you can imbibe from his life? [CBSE 2016] 44. At a certain time in Gir Forest of Gujarat, the number of heads and the number of legs of lions and human visitors were counted and it was found that there were 53 heads and 148legs. Find the number of lions and human visitors in the forest. What is the purpose of creating national forest? [CBSE 2016] Solutions 1. Given equations: x y  14