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Sorry for the title, I don't know how else to put this into words.

Basically I wanted to know how to get the result below:

enter image description here

I have no idea about why the graph is showing X as a diagonal line. How can X by itself be a line which is not constant?

Delta
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    The diagonal line is the line $y=x$. Where it meets the other line is where the $x$ values are the same. – The Count Jul 03 '19 at 01:05

2 Answers2

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$$x=462+0.085x$$ $$(1-0.085)x=462$$ $$0.915x=462$$ $$x=\frac{462}{0.915}=\frac{30800}{61}$$

azif00
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  • Ok. I guess I just lack very basic arithmetic knowledge. I'm having trouble visualizing how do you go from the first line to the second one. – Delta Jul 03 '19 at 01:09
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    From the first equation, substract $0.085x$ to both sides and note that $$x-0.085x=(1-0.085)x$$ – azif00 Jul 03 '19 at 01:11
  • Great! I see it now. Thank you very much – Delta Jul 03 '19 at 01:20
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Here you want to solve $$x=462+0.085x$$ There are two equations $y=x$ and $y=462+0.085x$.

Solving for $x=462+0.085x$ is equivalent to determining the solutions for the system $$y=x \text{ (Denoted by Blue Line) }$$

&

$$y=462+0.085x\text{ (Denoted by Red Line) }$$

The point of intersection of those two lines is your solution. Now we proceed to find the solution. $$(1-0.085)x=462$$ $$0.915x=462$$ $$x=\frac{462}{0.915}=\frac{30800}{61}$$

GraduateStudent
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