January 2026

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: \[ x\left(a-b+\frac{ab}{a-b}\right) = y\left(a+b-\frac{ab}{a-b}\right), \\ x + y = 2a^2 \] Solution Step 1: Simplify the Coefficients \[ a-b+\frac{ab}{a-b} = \frac{(a-b)^2 + ab}{a-b} = \frac{a^2 – ab + b^2}{a-b} \] \[ […]

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: \[ (a+2b)x + (2a-b)y = 2 \\ , (a-2b)x + (2a+b)y = 3 \] 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: \[ 5ax + 6by = 28 \\ , 3ax + 4by = 18 \] Solution Step 1: Reduce the Equations Let \[ X = ax,\quad Y = by \] Then the

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: \[ 2ax + 3by = a + 2b \\ , 3ax + 2by = 2a + b \] 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: \[ \frac{x}{a} = \frac{y}{b}, \\ ax + by = a^2 + b^2 \] Solution Step 1: Convert the First Equation into Linear Form From \[ \frac{x}{a} = \frac{y}{b} \] cross-multiplying, we

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: \[ \frac{x}{a} + \frac{y}{b} = a + b,\quad \frac{x}{a^2} + \frac{y}{b^2} = 2 \] Solution Step 1: Substitute Variables Let \[ \frac{x}{a} = u,\quad \frac{y}{b} = v \] Then the given

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: \[ \frac{x}{a} + \frac{y}{b} = 2, \\ ax – by = a^2 – b^2 \] Solution Step 1: Reduce to Linear Equations Multiply the first equation by \(ab\): \[ bx +

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: \[ \frac{57}{x+y} + \frac{6}{x-y} = 5,\quad \frac{38}{x+y} + \frac{21}{x-y} = 9 \] Solution Step 1: Substitute Variables Let \[ \frac{1}{x+y} = u,\quad \frac{1}{x-y} = v \] Then the given equations become:

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 \(y \neq 0\)): \[ \frac{2}{x} + \frac{3}{y} = 13,\quad \frac{5}{x} – \frac{4}{y} = -2 \] Solution Step 1: Substitute Variables Let \[ \frac{1}{x} = u,\quad \frac{1}{y}

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,