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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 (where \(x \neq 0\) and \(y \neq 0\)): \[ \frac{5}{x+y} – \frac{2}{x-y} = -1, \quad \frac{15}{x+y} + \frac{7}{x-y} = 10 \] Solution Step 1: Substitute Variables Let \[ \frac{1}{x+y} = u, […]

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: \[ ax + by = a^2 \\ , bx + ay = b^2 \] Solution Step 1: Compare with the Standard Form The standard form is: \[ a_1x + b_1y =

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: \[ x + ay = b \\ , ax – by = c \] Solution Step 1: Compare with the Standard Form The standard form is: \[ a_1x + b_1y =

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: \[ ax + by = a – b \\ , bx – ay = a + b \] Solution Step 1: Compare with the Standard Form The standard form is: \[

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: \[ \frac{x+y}{xy} = 2,\quad \frac{x-y}{xy} = 6 \] Solution Step 1: Simplify the Equations Multiply both equations by \(xy\): \[ x + y = 2xy \quad \text{(1)} \] \[ x –

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: \[ 2x – y = 6 \\ , x – y = 2 \] Solution Step 1: Compare with the Standard Form The standard form is: \[ a_1x + b_1y =

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: \[ 2x + y = 35 \\ , 3x + 4y = 65 \] Solution Step 1: Compare with Standard Form The standard form is: \[ a_1x + b_1y = c_1

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),