Educational

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:

Solve the System of Equations by the Substitution Method Video Explanation Question Solve the following system of equations: \[ 23x – 29y = 98, \\ 29x – 23y = 110 \] Solution Step 1: Express One Variable in Terms of the Other Subtract the first equation from the second: \[ (29x – 23y) – (23x

Solve the System of Linear Equations Using Elimination Method Video Explanation Watch the video below to understand the complete solution step by step: Solution Question: Solve the following system of equations: 99x + 101y = 499  …… (1) 101x + 99y = 501  …… (2) Step 1: Subtract Equation (1) from Equation (2) (101x +

Solve the System of Equations by the Substitution Method Video Explanation Question Solve the following system of equations: \[ 152x – 378y = -74, \\ -378x + 158y = -604 \] Solution Step 1: Express One Variable in Terms of the Other From the first equation: \[ 152x – 378y = -74 \] \[ 152x