What is the Method of Cross-Multiplication?
The Method of Cross-Multiplication is a structured, formula-driven method used to solve simultaneous linear equations. Instead of deciding whether to add, subtract, or substitute, this method provides a fixed matrix-like diagrammatic formula where you directly plug in the numerical coefficients to find the values of x and y immediately.
To use this method properly, both equations must first be written in their standard, uniform layout. The standard format requires all variables and constant numbers to sit on the left side of the equals sign, leaving exactly zero on the right side:
Equation 1: a1(x) + b1(y) + c1 = 0
Equation 2: a2(x) + b2(y) + c2 = 0
Here, the letters a, b, and c represent the fixed real number numbers (coefficients and constants) from the equations. The indices 1 and 2 simply track which equation the number came from. The cross-multiplication formula states that the ratios of the variables to the cross-products of their non-corresponding coefficients are completely equal.