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 + […]

Area of Triangle Formed by Three Lines Video Explanation Question Find the area of the triangle formed by the lines \(y = x\), \(x = 6\), and \(y = 0\). Solution Step 1: Find Points of Intersection Intersection of \(y = x\) and \(y = 0\): \[ x = 0 \Rightarrow (0,0) \] Intersection of

Area of Triangle Formed by Line with Axes Video Explanation Question Find the area of the triangle formed by the line \(\frac{x}{a} + \frac{y}{b} = 1\) with the coordinate axes. Solution Step 1: Identify Intercepts Given equation: \[ \frac{x}{a} + \frac{y}{b} = 1 \] x-intercept: \( (a, 0) \) y-intercept: \( (0, b) \) Step

Consistent Pair of Linear Equations Video Explanation Question If a pair of linear equations in two variables is consistent, then the lines represented by the equations are: (a) intersecting (b) parallel (c) always coincident (d) intersecting or coincident Solution Step 1: Meaning of Consistent System A system is said to be consistent if it has

Finding Relation Between a and b for Coincident Lines Video Explanation Question If the equations \(2x – 3y = 7\) and \((a+b)x – (a+b-3)y = 4a + b\) represent coincident lines, find the relation between \(a\) and \(b\). Solution Step 1: Write in Standard Form \[ 2x – 3y – 7 = 0 \] \[

Finding Value of k for No Solution Video Explanation Question Find the value of \(k\) for which the system of equations \(x + 2y = 5\) and \(3x + ky + 15 = 0\) has no solution. Solution Step 1: Write in Standard Form \[ x + 2y – 5 = 0 \] \[ 3x

Finding Relation Between a and b for Infinite Solutions Question If the system of equations \(2x + 3y = 7\) and \(2ax + (a+b)y = 28\) has infinitely many solutions, find the relation between \(a\) and \(b\). Solution Step 1: Write in Standard Form \[ 2x + 3y – 7 = 0 \] \[ 2ax

Condition for Unique Solution Video Explanation Question If \(am \ne bl\), then the system of equations \(ax + by = c\) and \(lx + my = n\) has: (a) a unique solution (b) no solution (c) infinitely many solutions (d) may or may not have a solution Solution Step 1: Identify Coefficients For equation (1):

Finding Value of k for Inconsistent System Video Explanation Question Find the value of \(k\) for which the system of equations \(3x + y = 1\) and \((2k – 1)x + (k – 1)y = 2k + 1\) is inconsistent. Solution Step 1: Write in Standard Form \[ 3x + y – 1 = 0

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 +