Method of Elimination The method of elimination is a technique used to solve a system of linear equations by transforming it into an equivalent system wi...
The method of elimination is a technique used to solve a system of linear equations by transforming it into an equivalent system with the same solution. This method involves manipulating the equations to create "equal" or "opposite" terms in the variables, allowing us to eliminate one variable and solve for the remaining one.
How it works:
We write the two linear equations in the same format (y = mx + b).
We add or subtract these equations to eliminate one variable.
The resulting equation is a single linear equation in one variable.
Solving this single equation gives us the value of that variable in terms of the other.
We substitute this value back into either of the original equations to find the other variable's value.
Benefits of using the method of elimination:
Simplifies the system of equations.
Allows us to solve linear equations even when there are multiple variables.
Provides a systematic approach to eliminate variables.
Example:
Solve the following system of linear equations using the method of elimination:
x + y = 5
x - y = 1
Solution:
Add the two equations together:
(x + y) + (x - y) = 5 + 1
2x = 6
x = 3
Substitute x = 3 into either of the original equations to find y:
3 + y = 5
y = 2
Therefore, the solution to the system of equations is x = 3 and y = 2