14Example: Addition method

The birthday example is now also solved using the addition method.

You have already seen the linear system of equations for this problem in this course:

$\def\arraystretch{1.25} \begin{array}{lrrlrrl}\mathrm{I} &2v&+&1.5m &= &150 \\\mathrm{II} &m&+&3 &= &v&-&2\end{array}$

Step 0: Clean up the equation and select a variable

$\def\arraystretch{1.25} \begin{array}{lrrlrrl}\mathrm{I} &2v&+&1.5m &= &150 \\\mathrm{II} &m&+&3 &= &v&-&2\;&\qquad|-3\quad|-v\end{array}$

$\def\arraystretch{1.25} \begin{array}{lllll}\mathrm{I} &2v&+&1.5m &= &150 \\\mathrm{II} &-v&+&m &=& -5\end{array}$

Now the equations are tidy and you have to select one of the variables. It is important to select the variable so that the next steps are as easy as possible. Remember: It's all a matter of practice!

Multiplying is usually easier than dividing, that's why the variable v was chosen here.

In the equation $\mathrm{I}$ you have: $\;\;\color{#009999}{2} \cdot v$

In the equation $\mathrm{II}$ you have: $\;\color{#009999}{1} \cdot v$

So you have to calculate $\mathrm{II} \cdot 2$.

1st step: multiply the equation $\mathrm{II}$

$\def\arraystretch{1.25} \begin{array}{lcccccl}\mathrm{II}& -v&+&m&=&-5& \quad &|\cdot 2\\\mathrm{II}' &-2v& + &2m &= &-10& \end{array}$