Condition for Unique Solution of a Pair of Linear Equations Video Explanation Question Find the value of \(k\) for which the following system of equations has a unique solution: \[ x + 2y = 3, \qquad 5x + ky + 7 = 0 \] Solution Step 1: Write in Standard Form \[ x + 2y […]
Condition for Unique Solution of a Pair of Linear Equations Video Explanation Question Find the value of \(k\) for which the following system of equations has a unique solution: \[ 4x – 5y = k, \qquad 2x – 3y = 12 \] Solution Step 1: Write in Standard Form \[ 4x – 5y – k
Condition for Unique Solution of a Pair of Linear Equations Video Explanation Question Find the value of \(k\) for which the following system of equations has a unique solution: \[ 4x + ky + 8 = 0, \qquad 2x + 2y + 2 = 0 \] Solution Step 1: Identify Coefficients From the given equations,
Condition for Unique Solution of a Pair of Linear Equations Video Explanation Question Find the value of \(k\) for which the following system of equations has a unique solution: \[ kx + 2y = 5, \qquad 3x + y = 1 \] Solution Step 1: Write in Standard Form \[ kx + 2y – 5
Consistency of a Pair of Linear Equations Video Explanation Question Determine whether the following system of equations has a unique solution, no solution or infinitely many solutions. If it has a unique solution, find it: \[ x – 2y = 8, \qquad 5x – 10y = 10 \] Solution Step 1: Write in Standard Form
Consistency of a Pair of Linear Equations Video Explanation Question Determine whether the following system of equations has a unique solution, no solution or infinitely many solutions. If it has a unique solution, find it: \[ 3x – 5y = 20, \qquad 6x – 10y = 40 \] Solution Step 1: Write in Standard Form
Consistency of a Pair of Linear Equations Video Explanation Question Determine whether the following system of equations has a unique solution, no solution or infinitely many solutions. If it has a unique solution, find it: \[ 2x + y = 5, \qquad 4x + 2y = 10 \] Solution Step 1: Write in Standard Form
Consistency of a Pair of Linear Equations Video Explanation Question Determine whether the following system of equations has a unique solution, no solution or infinitely many solutions. If it has a unique solution, find it: \[ x – 3y = 3, \qquad 3x – 9y = 2 \] Solution Step 1: Write in Standard Form
Solve the System of Equations by the Method of Cross-Multiplication Video Explanation Question Solve the following system of equations by the method of cross-multiplication: \[ \frac{b}{a}x + \frac{a}{b}y = a^2 + b^2, \\ x + y = 2ab \] Solution Step 1: Convert the First Equation into Linear Form Multiply the first equation by \(ab\):
Solve the System of Equations by the Method of Cross-Multiplication Video Explanation Question Solve the following system of equations by the method of cross-multiplication: \[ \frac{ax}{b} – \frac{by}{a} = a + b, \\ ax – by = 2ab \] Solution Step 1: Convert the First Equation into Linear Form Multiply the first equation by \(ab\):