Pair of Linear Equations

Important Questions

Q) If three times the greater of two numbers is divided by the smaller one, we get 4 as the quotient and 3 as the…

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Q) Explain why 7 × 11 × 13 + 13 and 7 × 6 × 5 × 4 × 3 × 2 × 1 +…

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Q) Three consecutive integers are such that sum of the square of second and product of other two is 161. Find the three integers. Ans:…

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Q) If the length of a rectangle is reduced by 5 cm and its breadth is increased by 2 cm, then the area of the…

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Q) Can the number (15n), n being a natural number, end with the digit 0 ? Ans:  For any number to end with the digit…

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Q) Check whether 6n can end with the digit 0 for any natural number n. Ans:  For any number to end with the digit 0, it…

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Q) The age of the father is twice the sum of the ages of his two children. After 20 years, his age will be equal…

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Q) In a 2-digit number, the digit at the unit’s place is 5 less than the digit at the ten’s place. The product of the…

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Q) Tara scored 40 marks in a test, getting 3 marks for each right answer and losing 1 mark for each wrong answer. Had 4…

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Q) 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.…

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Q) Solve the following system of linear equations : 2 x + 5 y = – 4 and 4 x – 3 y = 5…

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Q) Solve the following system of linear equations : 7 x – 2 y = 5 and 8 x + 7 y = 15 and…

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Q) Solve the following system of linear equations : 2p + 3q = 13 and 5p – 4q = – 2 Ans: Given equations are:…

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Q) In a chemistry lab, there is some quantity of 50% acid solution and some quantity of 25% acid solution. How much of each should…

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Q) The monthly incomes of A and B are in the ratio 8 : 7 and their expenditures are in the ratio 19 : 16.…

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Q) Solve the following pair of linear equations: Ans:  Given the equations: ……….. (i) ………….(ii) Step 1: Let’s multiply equation (i) by b2  and add…

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Q) Solve the following pair of linear equations: (a – b) x + (a + b) y = a2 – 2 a b – b2…

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Q) Solve the following pair of linear equations: 152x – 378y = – 74– 378 x + 152y = – 604 Ans:  Given the equations:…

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Q) Solve the following pair of linear equations: ax + by = c  bx + ay = 1 + c Ans:  Given the equations: a x + b…

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Q) Solve the following pair of linear equations:px + qy = p – qqx – py = p + q Ans:  Given the equations: Solve…

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Q) Find two consecutive odd positive integers, the sum of whose squares is by using the quadratic formula. Ans:  Let’s consider the 1st odd positive…

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Q) The product of Rehan’s age (in years) 5 years ago and his age 7 years from now, is one more than twice his present…

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Q) ABCD is a rectangle if the value of AB= 12 is given, find the values of x and y. Ans:  We know, opposite sides…

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Q) Mrs. Gupta arranged some snacks for her child’s birthday party. After the guest left she had some food left over. She did not want to…

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Q) A number consists of two digits. Where the number is divided by the sum of its digits, the quotient is 7. If 27 is subtracted…

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Q) The sum of ages of a father and his son is 45 years. Five years ago, the product of their ages (in years) was…

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Q) A fraction becomes when 1 is subtracted from the numerator. It becomes when 8 is added to the denominator. Find the fraction. Ans: Let’s…

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Q) Using graphical method, find whether following system of linear equations x = 0 and y = – 7 is consistent or not. Ans:  Draw…

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Q) Two pipes together can fill a tank in hours. The pipe with larger diameter takes 2 hours less than the pipe with smaller diameter…

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Q) A train travels at a certain average speed for a distance of 54 km and then travels a distance of 63 km at an average…

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Q) Two people are 16 km apart on a straight road. They start walking at the same time. If they walk towards each other with different…

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Q) Two schools ‘P’ and ‘Q’ decided to award prizes to their students for two games of Hockey Rs. x per student and Cricket Rs. y…

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Q) If 217x + 131y = 913 and 131x + 217y = 827, then solve the equations for the values of x and y. Ans: 217…

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Q) If the system of linear equations 2x+3y= 7 and 2ax + (a + b) y = 28 have infinite number of solutions, then find…

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Q)Jaya scored 40 marks in a test getting 3 marks for each correct answer and losing 1 mark for each incorrect answer., Had 4 marks…

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Q)Solve the pair of equations x = 5 and y = 7 graphically. Ans:  Plot both the equations on the graph. Increase till intersection point…

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Q) Using graphical method, find whether following system of linear equations x = 0 and y = – 3 is consistent or not. Ans:  Draw…

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Q) Half of the difference between two numbers is 2. The sum of the greater and twice the smaller number is 13. Find the numbers.…

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Q) Solve the pair of equations x = 3 and y = – 4 graphically.  Ans: Lets plot both the equations on the graph. Increase…

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