Finding Values of a and b for Infinite Solutions Video Explanation Question If the system of equations \(2x + 3y = 7\) and \((a+b)x + (2a-b)y = 21\) has infinitely many solutions, find \(a\) and \(b\). Solution Step 1: Write in Standard Form \[ 2x + 3y – 7 = 0 \] \[ (a+b)x + […]
Finding Value of k for No Solution Video Explanation Question Find the value of \(k\) for which the system of equations \(x + 2y – 3 = 0\) and \(5x + ky + 7 = 0\) has no solution. Solution Step 1: Identify Coefficients For equation (1): \(a_1 = 1,\; b_1 = 2,\; c_1 =
Finding Value of k for Infinite Solutions Video Explanation Question Find the value of \(k\) for which the system of equations \(2x + 3y = 5\) and \(4x + ky = 10\) has infinitely many solutions. Solution Step 1: Write in Standard Form \[ 2x + 3y – 5 = 0 \] \[ 4x +
Finding Value of k for Unique Solution Video Explanation Question Find the value of \(k\) for which the system of equations \(kx – y = 2\) and \(6x – 2y = 3\) has a unique solution. Solution Step 1: Write in Standard Form \[ kx – y – 2 = 0 \] \[ 6x –
Finding Fixed Charge and Extra Day Rent Video Explanation Question A shopkeeper charges a fixed amount for the first 2 days and an additional charge per day after that. Latika pays ₹22 for 6 days. Anand pays ₹16 for 4 days. Find the fixed charge and the charge per extra day. Solution Step 1: Let
Finding Number of Correct Answers Video Explanation Question In a competitive examination: 1 mark is awarded for each correct answer and \( \frac{1}{2} \) mark is deducted for each wrong answer. Jayanti answered 120 questions and scored 90 marks. Find the number of correct answers. Solution Step 1: Let Variables Let number of correct answers
Finding Cost Price and Marked Price Video Explanation Question A shopkeeper sells a saree at 8% profit and a sweater at 10% discount, getting ₹1008. If she sold the saree at 10% profit and the sweater at 8% discount, she would get ₹1028. Find the cost price of the saree and the list price of
Finding Capital of Two Persons Video Explanation Question One person says: “Give me ₹100, I shall become twice as rich as you.” The other replies: “If you give me ₹10, I shall be six times as rich as you.” Find their respective capitals. Solution Step 1: Let Variables Let first person’s capital = \(x\) Let
Finding Number of Students in a Class Video Explanation Question Students are arranged in rows. If 3 students are extra in each row, there is 1 row less. If 3 students are less in each row, there are 2 rows more. Find the total number of students. Solution Step 1: Let Variables Let number of