- Math Lessons
- >
- Algebra
- >
- Solving System of Linear Equations
- >
- Elimination Method

« Substitution Method |

Solving System of Linear Equations: (lesson 2 of 5)

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).**

Level 1

Level 2