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: x = 2

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 (x, y) = (2, 1).

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: y = -2

Take the value for y and substitute it back into either one of the original equations.

The solution is (x, y) = (1, -2).

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 (x, y) = (3, -1).