Elimination Method The elimination method is a technique used to eliminate two equations in two variables. This method involves adding or subtracting the two...
The elimination method is a technique used to eliminate two equations in two variables. This method involves adding or subtracting the two equations to eliminate the variable in one equation. The resulting equation is then solved for the remaining variable, and the values of the other variables can then be found by plugging the values of the first variable back into the original equations.
How it works:
We start by adding or subtracting the two equations together.
We then isolate one variable in one of the equations.
We substitute the expression for that variable into the other equation.
We solve the resulting equation for the remaining variable.
We plug in the values of the first variable we isolated into the original equations to find the values of the other variables.
Examples:
Elimination Method Example 1:
Equations:
2x + 3y = 11
4x - 2y = 3
Adding the two equations together:
(2x + 3y) + (4x - 2y) = 11 + 3
6x = 14
Dividing both sides by 6:
Elimination Method Example 2:
Equations:
x + y = 5
2x - y = 1
Subtracting the second equation from the first equation:
(x + y) - (2x - y) = 5 - 1
-x = 4
Multiplying both sides by -1:
Benefits of the Elimination Method:
Can be used to eliminate any number of variables.
The method is systematic and easy to follow.
It is a versatile technique that can be used with various types of linear equations.
Note: The elimination method can be used with any two linear equations in two variables, as long as the equations have the same variables in the same positions