Find the intersection or the solution to the following system of equations: and

As we did with a set of two equations, first line up the equations to choose the variable that we wish to eliminate:

For these equations, it looks easiest to eliminate the -variable. To do this, add the first and second equations together and then add the second and third equations together:

Now, you are left with and We now solve these as done previously with a set of two equations:

Multiply either the top or the bottom equation by −1 to eliminate the -variable.

Next, find using one of or and the solution looks to be the easiest to work with.

Finally,  find using one of the original three equations:

These planes intersect at the point and , or the coordinate

Find the intersection or the solution to the following system of equations: and

First, line up the equations to choose the variable that we wish to eliminate:

In this example, adding the first and last equations eliminates the variable without having to modify any of the equations:

Now, there are two equations left:

First multiply the bottom equation by −3, then add it to the top equation, to eliminate the variable :

Now choose one of the two remaining equations, or to find the variable Choosing leaves:

Finally, to find the third variable, use one of the original three equations:   or Choosing gives:

These planes intersect at the point and or the coordinate