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Elimination Method
The elimination method of solving systems of equations is also called the addition method. To solve a system of equations by elimination we transform the system such that one variable "cancels out".
Example 1: Solve the system of equations by elimination
Solution:
In this example we will "cancel out" the y term. To do so, we can add the equations together.
Now we can find:
In order to solve for y, take the value for x and substitute it back into either one of the original equations.
The solution is
Example 2: Solve the system using elimination
Solution:
Look at the x - coefficients. Multiply the first equation by -4, to set up the x-coefficients to cancel.
Now we can find:
Take the value for y and substitute it back into either one of the original equations.
The solution is
Example 3: Solve the system using elimination method
Solution:
In this example, we will multiply the first row by -3 and the second row by 2; then we will add down as before.
Now we can find: y = -1
Substitute y = -1 back into first equation:
The solution is
Exercise: Solve the following systems using elimination method
Level 1
Level 2