Let x be the number of minutes spent swimming and y be the number of minutes spent biking.
Since the time Dylan spends swimming must be no less than twice the time he spends biking, you obtain the unequality [tex]x\ge 2y[/tex]
If Dylan
works out and burns 10 calories per minute swimming, then he burns 10x calories per x minutes and if Dylan
works out and burns 7 calories per
minute biking, then he burns 7y calories per y minutes. He wants to burn a minimum of 600 calories, then total amount of calories he burns is [tex]10x+7y\ge 600[/tex].
You have the following system: [tex] \left \{ {{x\ge 2y} \atop {10x+7y\ge 600}} \right. [/tex]. The graphical interpretation see on the picture.
Let's solve the system: [tex] \left \{ {{x=2y} \atop {10x+7y=600}} \right. [/tex]. If x=2y, then 20y+7y=600, 27y=600, [tex]y= \frac{200}{9} [/tex] and [tex]x= \frac{400}{9} [/tex] is the minimal number of minutes, that Dylan has to spend biking and swimming.
Also you can take any point from the shaded domian (see picture), for example x=70, y=20.
