Pair of Linear Equations in Two Variables

CBSE Class 10 Mathematics · 82 board questions from this chapter; 81 listed below, 2022–2026

• The pair of linear equations (3 x)/2+(5 y)/3=7 and 9 x+10 y=14, is:2026
• The value of k for which the system of linear equations k x-y-2=0 and 6 x-2 y-3=0 has infinitely many solutions, is (does)2026
• If a pair of linear equations in two variables is represented by two coincident lines, then the pair of equations has:2026
• If the pair of linear equations: a_1 x+b_1 y+c_1=0 and a_2 x+b_2 y+c_2=0 is consistent and dependent, then2026
• The value of k for which the system of linear equations x/2+y/3=5 and 2 x+ky=7 is inconsistent, is2026
• Equation of a line coincident with 2 · 5 x-2 y=3 is:2026
• Assertion: The system of linear equations 3 x-5 y+7=0 and -6 x+10 y+14=0 is inconsistent. Reason (R): When two linear equations…2026
• In a class test, Veer scored 6 more than twice as many marks as Kevin scored. If one of them had scored 4 more marks, their total…2026
• Use graphical method to solve the system of linear equations: x=-3 and 5 x-2 y=-5.2026
• Use graphical method to solve the system of linear equations: y=-3 and x+2 y=4.2026
• Solve the system of linear equations: x=4 and 3 x-2 y=6 graphically.2026
• A person on tour has ₹ 5,400 for his expenses. If he extends his tour by 5 days, he has to cut down his daily expenses by ₹ 180.…2026
• Aarush bought 2 pencils and 3 chocolates for ₹ 11 and Tanish bought 1 pencil and 2 chocolates for ₹ 7 from the same shop.…2026
• Draw the graph of the pair of linear equations x-y+2=0 and 4 x-y-4=0. Calculate the area of the triangle formed by the lines so…2026
• Represent the following pair of linear equations graphically and hence comment on the condition of consistency of this pair: x-5…2026
• Solve the following system of equations graphically: 2 x+3 y=5,-3 x+y=-2 OR The sum of the digits of a 2-digit number is 11. The…2026
• The system of equations x+5=0 and 2 x-1=0, has2025
• If x=1 and y=2 is a solution of the pair of linear equations 2 x-3 y+a=0 and 2 x+3 y-b=0, then:2025
• The value of'k'for which the system of linear equations 6 x+y=3k and 36 x+6 y=3 have infinitely many solutions is:2025
• The value of ' p ' for which the equations p x+3 y=p-3,12 x+p y=p has infinitely many solutions is:2025
• A system of two linear equations in two variables is inconsistent, if the lines in the graph are:2025
• The system of equations y+a=0 and 2 x=b has2025
• The line represented by the equation x-y=0 is:2025
• The system of equations 2 x+1=0 and 3 y-5=0 has2025
• Assertion: The pair of linear equations px + 3y + 59=0 and 2 x+6 y+118=0 will have infinitely many solutions if p=1. Reason (R):…2025
• Solve the following pair of equations algebraically: 101 x+102 y=304; 102 x+101 y=305 OR In a pair of supplementary angles, the…2025
• Solve the following system of equations algebraically: 30 x+44 y=10; 40 x+55 y=132025
• The cost of 2 kg apples and 1 kg of grapes on a day was found to be ₹ 320. The cost of 4 kg apples and 2 kg grapes was found to…2025
• Solve the following system of equations algebraically: 37 x+63 y=137 63 x+37 y=1632025
• Solve the following system of equations algebraically: 73 x-37 y=109 37 x-73 y=12025
• Check whether the given system of equations is consistent or not. If consistent, solve graphically. x-2 y=0; 2 x+y=02025
• The monthly incomes of two persons are in the ratio 9: 7 and their monthly expenditures are in the ratio 4: 3. If each saved ₹…2025
• Check whether the following pair of equations is consistent or not. If consistent, solve graphically x+3 y=6; 3 y-2 x=-122025
• Solve the following system of equations graphically: 2 x-y-2=0; -4 x+y+4=0 Also, find the absolute difference between the…2025
• The two angles of a right angled triangle other than 90° are in the ratio 2: 3. Express the given situation algebraically as a…2025
• Solve the following system of equations graphically: 2 x+y=5 and 4 x-y=7. Hence, write the coordinates of the points where given…2025
• Check whether the following system of equations is consistent or not. If consistent, solve graphically x-2 y+4=0,2 x-y-4=02025
• The perimeter of a rectangle is 70 cm. The length of the rectangle is 5 cm more than twice is breadth. Express the given…2025
• Solve the following system of equations graphically: 2 x+3 y=6; x+y-1=0 Also, find the sum of ordinates of the points where given…2025
• Vijay invested certain amounts of money in two schemes A and B, which offer interest at the rate of 8\% per annum and 9\% per…2025
• A 2-digit number is seven times the sum of its digits and two (2) more than 5 times the product of its digits. Find the number.…2025
• The sum of the areas of two squares is 52 cm^2 and difference of their perimeters is 8 cm. Find the lengths of the sides of the…2025
• The students of a class are made to stand equally in rows. If 3 students are extra in each row, there would be 1 row less. If 3…2025
• A bag contains some red and blue balls. Ten percent of the red balls, when added to twenty percent of the blue balls, give a…2025
• A man lent a part of his money at 10\% p.a. and the rest at 15\% p.a. His income at the end of the year is ₹ 1,900. If he had…2025
• A two-digit number is such that the product of its digits is 12. When 36 is added to this number, the digits interchange their…2025
• The numerator of a fraction is 3 less than its denominator. If 2 is added to both numerator and denominator, then the sum of the…2025
• A school is organizing a grand cultural event to show the talent of its students. To accommodate the guests, the school plans to…2025
• The value of k for which the system of equations 3 x-y+8=0 and 6 x-ky+16=0 has infinitely many solutions, is2024
• The pair of linear equations x+2 y+5=0 and -3 x=6 y-1 has2024
• The pair of linear equations y=0 and y=-7 have2024
• Which out of the following type of straight lines will be represented by the system of equations 3 x+4 y=5 and 6 x+8 y=7?2024
• If a pair of linear equations in two variables is consistent, then the lines represented by the two equations are:2024
• Two lines are given to be parallel. The equation of one of these lines is 5 x-3 y=2. The equation of the second line can be:2024
• In the given figure, graphs of two linear equations are shown. The pair of these linear equations is:2024
• Solve the following system of linear equations 7 x-2 y=5 and 8 x+7 y=15 and verify your answer.2024
• Solve the following system of linear equations: 2 p+3 q=13 and 5 p-4 q=-22024
• Solve the following system of linear equations algebraically: 2 x+5 y=-4; 4 x-3 y=52024
• The sum of the digits of a 2-digit number is 14. The number obtained by interchanging its digits exceeds the given number by 18.…2024
• Rehana went to a bank to withdraw ₹ 2,000. She asked the cashier to give her ₹ 50 and ₹ 100 notes only. Rehana got 25 notes in…2024
• Solve the following system of linear equations graphically: x-y+1=0; x+y=52024
• Three years ago, Rashmi was thrice as old as Nazma. Ten years later, Rashmi will be twice as old as Nazma. How old are Rashmi and…2024
• Using graphical method, solve the following system of equations: 3 x+y+4=0 and 3 x-y+2=0 OR Tara scored 40 marks in a test,…2024
• In a flight of 2800 km, an aircraft was slowed down due to bad weather. Its average speed is reduced by 100 km/h and by doing so,…2024
• A 2-digit number is such that the product of the digits is 14. When 45 is added to the number, the digits are reversed. Find the…2024
• Using graphical method, solve the following system of equations: 3 x-2 y=10 and 5 x+3 y=4 OR If three times the greater of two…2024
• The pair of equations ax+2 y=9 and 3 x+by=18 represent parallel lines, where a, b are integers, if:2023
• The value of k for which the pair of equations k x=y+2 and 6 x=2 y+3 has infinitely many solutions,2023
• If 2 x+3 y=15 and 3 x+2 y=25, then the value of x-y is:2023
• If the pair of equations 3 x-y+8=0 and 6 x-ry+16=0 represent coincident lines, then the value of 'r' is:2023
• The pair of linear equations 2 x=5 y+6 and 15 y=6 x-18 represents two lines which are:2023
• The pair of equations x=a and y=b graphically represents lines which are:2023
• 3 chairs and 1 table cost ₹ 900; whereas 5 chairs and 3 tables cost ₹ 2,100. If the cost of 1 chair is ₹ x and the cost of 1…2023
• The solution of the pair of equations x+y=a+b and ax-by=a^2-b^2 is:2023
• The condition for the system of linear equations a x+by=c; l x+my=n to have a unique solution is2023
• Solve the pair of equations x=3 and y=-4 graphically. OR Using graphical method, find whether following system of linear…2023
• Solve the pair of equations x=5 and y=7 graphically. OR Using graphical method, find whether pair of equations x=0 and y=-3, is…2023
• A 2-digit number is seven times the sum of its digits. The number formed by reversing the digits is 18 less than the given…2023
• A fraction becomes 1/3 when 1 is subtracted from the numerator. It becomes 1/4 when 8 is added to the denominator. Find the…2023
• If the system of linear equations 2 x+3 y=7 and 2 a x+(a+b) y=28 have infinite number of solutions, then find the values of ' a '…2023
• A 2-digit number is such that the product of its digits is 24. If 18 is subtracted from the number, the digits interchange their…2022

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