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# Let x,y be two real numbers such that y−8x= 10 and (x−2)(y−2) is as small as possible. what is the value of 60x−2y?

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Let x,y be two real numbers such that y−8x= 10 and (x−2)(y−2) is as small as possible. what is the value of 60x−2y?

Apr 18, 2022

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what is the value of 60x−2y?

Hello Guest!

$$y=8x+10\\ (x−2)(y−2)=\color{blue}-18\ determined\ graphically\\ x=\frac{\color{blue}-18}{y-2}+2$$

$$x=0,5\\y=14$$

$$60x-2y=60\cdot0,5-2\cdot 14=2$$

!

Apr 18, 2022
edited by asinus  Apr 19, 2022