11Adding/Subtracting equations
You can add one equation to another. This gives you a new equation.
Why does this work?
Visually, you can imagine each equation as a scale. Each of its scales represents one side of the equation.
The equations of the scales are:
Scale 1:
Scale 2:
Then, put the contents of each of the left-hand sides and the contents of the right-hand sides together on a third scale. The balance remains in equilibrium!
Mathematically, it looks like this:
Scale 3:
The same way, you can subtract two equations from each other.
What happens when adding/subtracting equations?
When you add/subtract equations, you add/subtract two equations that become a new equation.
How is equality sustained?
Don't be confused by the fact that you have to add/subtract two equations instead of numbers as usual! To do this, consider the left and right sides of each equation as one coherent part.
You proceed as follows:
Add/subtract the respective left sides of the two equations and then conclude.
Add/subtract the respective right sides of the two equations and then conclude.
Put a between the new left and right sides, to obtain your new equation.
It is useful to "prepare" the equations before adding/subtracting them.
This means, for example, to put all variables (with their coefficients) on the left sides of the equations and all numbers without variables on the right sides.
In no time at all, you have easily added/subtracted two equations to create a new equation!
On the next page you will see how you can apply this new knowledge to solve linear systems.
