Graphical Solution of a Pair of Linear Equations Video Explanation Question Solve the following system of equations graphically: \[ x + y = 3 \] \[ 2x + 5y = 12 \] Solution Step 1: Write Both Equations Equation (1): \[ x + y = 3 \Rightarrow y = 3 – x \] Equation (2): […]

Algebraic and Geometrical Representation of Cost Problem Video Explanation Question The cost of 2 kg of apples and 1 kg of grapes on a day was ₹160. After a month, the cost of 4 kg of apples and 2 kg of grapes is ₹300. Represent the situation algebraically and geometrically. Solution Step 1: Define the

Pair of Linear Equations – Nature of Lines Video Explanation Question Given the linear equation \[ 2x + 3y – 8 = 0, \] write another linear equation in two variables such that the geometrical representation of the pair so formed is: (i) intersecting lines (ii) parallel lines (iii) coincident lines Solution Given Equation \[

Nature of Pair of Linear Equations Using Ratio of Coefficients Video Explanation Question On comparing the ratios \[ \frac{a_1}{a_2}, \frac{b_1}{b_2}, \frac{c_1}{c_2}, \] find out whether the lines representing the following pairs of linear equations intersect at a point, are parallel or coincide (without drawing them): (i) \(5x – 4y + 8 = 0,\; 7x +

Graphical Representation Using Ratio of Coefficients Video Explanation Question Gloria is walking along the path joining the points \((-2, 3)\) and \((2, -2)\), while Suresh is walking along the path joining \((0, 5)\) and \((4, 0)\). Represent this situation graphically and check the nature of the paths using the ratio of coefficients. Solution Step 1:

Graphical Representation of the Paths of Two Trains Video Explanation Question The path of train A is given by the equation \[ 3x + 4y – 12 = 0 \] and the path of another train B is given by \[ 6x + 8y – 48 = 0. \] Represent this situation graphically. Solution Step

Linear Equations in Two Variables – Algebraic and Graphical Representation Video Explanation Question Aftab tells his daughter, “Seven years ago, I was seven times as old as you were then. Also, three years from now, I shall be three times as old as you will be.” Represent this situation algebraically and graphically. Solution Step 1:

Algebraic and Graphical Representation Using Linear Equation in Two Variables Video Explanation Question Akhila went to a fair in her village. She enjoyed rides on the Giant Wheel and played Hoopla. The number of times she played Hoopla is half the number of rides she had on the Giant Wheel. Each ride costs ₹3 and

Verify that 1/2, 1 and −2 are the zeroes of the cubic polynomial f(x) = 2x³ + x² − 5x + 2 and verify the relationship between the zeroes and coefficients Video Explanation Watch the video explanation below: Given f(x) = 2x³ + x² − 5x + 2 The given zeroes are: 1/2, 1 and

Graph of a Quadratic Polynomial Video Explanation Question Which of the following is not the graph of a quadratic polynomial? Solution Key Property of a Quadratic Polynomial The graph of a quadratic polynomial \[ f(x) = ax^2 + bx + c \] is always a parabola which: opens upward or downward has exactly one turning