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: \[ 3x + 2y + 25 = 0 \\ , 2x + y + 10 = 0 \] Solution Step 1: Write the Equations in Standard Form \[ 3x + 2y […]

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: \[ x + 2y + 1 = 0 \\ , 2x – 3y – 12 = 0 \] Solution Step 1: Write the Equations in Standard Form \[ x + 2y

Pair of Linear Equations with a Given Unique Solution Video Explanation Question Write a pair of linear equations which has the unique solution \[ x = -1,\quad y = 3. \] How many such pairs can you write? Solution Step 1: Use the Given Solution Since the solution is \[ (x,\; y) = (-1,\; 3),

Equation of a Line Passing Through a Given Point Video Explanation Question Write an equation of a line passing through the point representing the solution of the pair of linear equations: \[ x + y = 2, \quad 2x – y = 1 \] How many such lines can we find? Solution Step 1: Find

Find the Values of x and y Video Explanation Question In a rectangle, the lengths of the sides are: \[ 13,\; 7,\; (x + 3y),\; (3x + y) \] Find the values of \(x\) and \(y\). Solution Step 1: Use the Property of a Rectangle Opposite sides of a rectangle are equal. Hence, \[ x

Solve the Pair of Linear Equations Video Explanation Question Solve the following pair of equations: \[ \frac{x}{10} + \frac{y}{5} – 1 = 0, \quad \frac{x}{8} + \frac{y}{6} = 15 \] Hence find the value of \(\lambda\) if \[ y = \lambda x + 5. \] Solution Step 1: Convert Equations into Standard Form First equation:

Find the Values of a and b Video Explanation Question If \(x + 1\) is a factor of \[ 2x^3 + ax^2 + 2bx + 1, \] find the values of \(a\) and \(b\) given that \[ 2a – 3b = 4. \] Solution Step 1: Use Factor Theorem Since \(x + 1\) is a

Solve the System of Equations by the Substitution Method Video Explanation Question Solve the following system of equations: \[ 21x + 47y = 110 \quad (1) \] \[ 47x + 21y = 162 \quad (2) \] Solution Step 1: Express One Variable in Terms of the Other From equation (1): \[ 21x = 110 –

Solve the System of Linear Equations by the Substitution Method Video Explanation Question Solve the following system of equations: \[ x – y + z = 4 \quad (1) \] \[ x + y + z = 2 \quad (2) \] \[ 2x + y – 3z = 0 \quad (3) \] Solution Step 1:

Solve the System of Linear Equations by the Substitution Method Video Explanation Question Solve the following system of equations: \[ x – y + z = 4 \quad (1) \] \[ x – 2y + 3z = 9 \quad (2) \] \[ 2x + y + 3z = 1 \quad (3) \] Solution Step 1: