Infinitely Many Solutions of a Pair of Linear Equations Video Explanation Question Find the values of \(a\) and \(b\) for which the following system of linear equations has infinitely many solutions: \[ (2a-3)x – 3y = 5, \qquad 3x + (b-2)y = 3 \] Solution Step 1: Write in Standard Form \[ (2a-3)x – 3y […]
Infinitely Many Solutions of a Pair of Linear Equations Video Explanation Question Find the values of \(p\) and \(q\) for which the following system of linear equations has infinitely many solutions: \[ 2x + 3y = 9, \qquad (p+q)x – (2p-q)y = 3(p+q+1) \] Solution Step 1: Write the Equations in Standard Form \[ 2x
Infinitely Many Solutions of a Pair of Linear Equations Video Explanation Question Find the values of \(a\) and \(b\) for which the following system of linear equations has infinitely many solutions: \[ 2x – 3y = 7, \qquad (a+b)x – (a+b-3)y = 4a + b \] Solution Step 1: Write in Standard Form \[ 2x
Infinitely Many Solutions of a Pair of Linear Equations Video Explanation Question Determine the values of \(a\) and \(b\) so that the following system of linear equations has infinitely many solutions: \[ (2a-1)x + 3y – 5 = 0, \qquad 3x + (b-1)y – 2 = 0 \] Solution Step 1: Identify Coefficients From the
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