## 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…

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

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:…

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…

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

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…

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…

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…

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…

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.…

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

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

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

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…

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

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…

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

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

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

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

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…

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…

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…

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…

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…

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…

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…

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

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…

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…

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…

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…

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

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

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…

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

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

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.…

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