15Example: Addition method

Step 2: Removing one variable

Now both equations have both the unknowns and the numbers below each other.

The signs of $vv$ are different, so you add the equations.

Now there is only one variable left!

Step 3: Determine the values of the two variables

First solve the equation from step 2

Substitute $mm$ into one of the two equations

For example, $mm$ substituted into $\mathrm{I}\mathrm{I}\backslash mathrm\{II\}$:

So again, the mother is 40 years old and the father is 45 years old!

$\mathbb{L}=\{(m\mathrm{\mid }v)=(40\mathrm{\mid }45)\}\backslash mathbb\{L\}=\backslash \{(m|v)=(\; \backslash color\{\#cc0000\}\{40\}|\; \backslash color\{\#009999\}\{45\})\backslash \}$.