Condition for Unique Solution of a Pair of Linear Equations Video Explanation Question Obtain the condition for the following system of linear equations to have a unique solution: \[ ax + by = c, \qquad lx + my = n \] Solution Step 1: Write in Standard Form \[ ax + by – c = […]
Condition for Coincident Lines Video Explanation Question For what value of \(k\), will the following system of equations represent coincident lines? \[ x + 2y + 7 = 0, \qquad 2x + ky + 14 = 0 \] Solution Step 1: Identify Coefficients From the given equations, \[ a_1 = 1, \quad b_1 = 2,
Consistency of a Pair of Linear Equations Video Explanation Question Find the values of \(k\) for which the system \[ 2x + ky = 1, \qquad 3x – 5y = 7 \] will have (i) a unique solution, (ii) no solution. Also, check whether there is a value of \(k\) for which the system has
Infinitely Many Solutions of a Pair of Linear Equations Video Explanation Question Find the value of \(c\) for which the following system of equations has infinitely many solutions: \[ cx + 3y + 3 – c = 0, \qquad 12x + cy – c = 0 \] Solution Step 1: Write in Standard Form \[
Infinitely Many Solutions of a Pair of Linear Equations Video Explanation Question Prove that there is a value of \(c\) (\(c \neq 0\)) for which the system \[ 6x + 3y = c – 3, \qquad 12x + cy = c \] has infinitely many solutions. Find this value. Solution Step 1: Write the Equations
Consistency of a Pair of Linear Equations Video Explanation Question Find the value of \(k\) for which the system of equations \[ kx + 2y = 5, \qquad 3x + y = 1 \] has (i) a unique solution (ii) no solution. Solution Step 1: Write in Standard Form \[ kx + 2y – 5
Condition for Inconsistency of a Pair of Linear Equations Video Explanation Question For what value of \( \alpha \) will the following system of equations be inconsistent (have no solution)? \[ \alpha x + 3y = \alpha – 3, \qquad 12x + \alpha y = \alpha \] Solution Step 1: Write in Standard Form \[
Condition for Inconsistency of a Pair of Linear Equations Video Explanation Question For what value of \(k\) will the following system of equations be inconsistent? \[ 4x + 6y = 11, \qquad 2x + ky = 7 \] Solution Step 1: Write in Standard Form \[ 4x + 6y – 11 = 0 \quad (1)
Condition for No Solution of a Pair of Linear Equations Video Explanation Question Find the value of \(k\) for which the following system of equations has no solution: \[ kx + 3y = k – 3, \qquad 12x + ky = 6 \] Solution Step 1: Write in Standard Form \[ kx + 3y –
Condition for No Solution of a Pair of Linear Equations Video Explanation Question Find the value of \(k\) for which the following system of equations has no solution: \[ 2x + ky = 11, \qquad 5x – 7y = 5 \] Solution Step 1: Write in Standard Form \[ 2x + ky – 11 =