Algebra Know-It-ALL

282 Larger Linear Systems

Get the equations into form

Now that we’ve chosen the variable to eliminate, we must get all three equations into the same

form. The following form is as good as any:

ax+by+cz=d

where a, b, c, and d are constants. The first equation is already in this form. The second

equation is

2 x− 5 y=z− 1

Subtracting z from each side will put it into the form we want:

2 x− 5 y−z=− 1

The third equation is

3 x=− 6 y+ 7 z

Adding 6y to each side, we get

3 x+ 6 y= 7 z

We can subtract 7z from each side and it comes into the sought-after form:

3 x+ 6 y− 7 z= 0

We now have the three-by-three system in this uniform condition:

− 4 x+ 2 y− 3 z= 5

2 x− 5 y−z=− 1

3 x+ 6 y− 7 z= 0

Make z vanish once

Here are the first two revised equations again, for reference:

− 4 x+ 2 y− 3 z= 5

and

2 x− 5 y−z=− 1