Bedrich and Adam

When Bedrich is as old as Adam today, Adam will be 14 years old. When Adam was as old as Bedrich, Bedrich was two years old today. How old are Adam and Bedrich today?

Correct answer:

a =  10
b =  6

Step-by-step explanation:

$$\begin{gathered} b+r=a \\ a+r=14 \\ b-r=2 \\ a-b-r=0 \\ a+r=14 \\ b-r=2 \\ Row2-Row1\to Row2 \\ a-b-r=0 \\ b+2r=14 \\ b-r=2 \\ Row3-Row2\to Row3 \\ a-b-r=0 \\ b+2r=14 \\ -3r=-12 \\ r=\frac{-12}{-3}=4 \\ b=14-2r=14-2\cdot 4=6 \\ a=0+b+r=0+6+4=10 \\ a=10 \\ b=6 \\ r=4 \end{gathered}$$

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