Method of Cross Multiplication Definition: The method of cross multiplication is a mathematical technique used to solve systems of linear equations invo...
Method of Cross Multiplication
Definition:
The method of cross multiplication is a mathematical technique used to solve systems of linear equations involving two or more variables. It involves multiplying the coefficients of each variable in the two equations to form a new matrix.
Steps:
Multiply the coefficients of x and y in the first equation.
Multiply the coefficients of x and y in the second equation.
Add the two products of the coefficients of x.
Add the two products of the coefficients of y.
Example:
Consider the following two linear equations:
x + y = 5
x - y = 1
Solution using cross multiplication:
| 1 & 1 | * | 5 |
| 1 & -1 | * | 1 |
Multiplying the coefficients, we get:
1 * 5 - 1 * 1 = 5 - 1 = 4
Therefore, the solution to the system of equations is x = 4 and y = 1.
Benefits of Cross Multiplication:
Helps to eliminate one variable by multiplying corresponding coefficients.
Provides a systematic way to solve systems of linear equations.
Can be applied to solve various types of linear equations, including those involving different variable combinations