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 November 20th, 2010, 07:23 PM #1 Newbie   Joined: Sep 2008 Posts: 4 Thanks: 0 Solution of y = x and y = -x I was helping someone with math and embarrassed myself today. I asked that person to use basic algebra to compute the distance between the line y = -x and the point (4,4). I told the person to:Compute the slope of all lines perpendicular to y = -x (we determined this was 1) Find a line with slope 1 that runs through point (4,4) (we determined this was the line y = x) Find where y = x and y = -x intersect. Find the distance between (the point defined by the intersection of y = x and y = -x) and (4,4) This process went pretty well until Step#3 above, where I embarrassed myself showing the person how to solve the linear system y = x y = -x My first instinct was to solve the system by substituting the first equation y = x into the second equation y = -x giving: x = -x but this is complete nonsense right of the bat! How can x = -x? If you divide both sides by x, then you get 1 = -1 which is even more bizarre. I guess I could try this: x = -x x+x=-x+x 2x=0 2x/2=0/2 x=0 ,but I still can't get over how x can ever be -x. Much to my embarrassment, this blows my mind. Can someone please explain to me how I can solve the system y=x y=-x without using a plotting or matrix algebra technique? Confused, bogger57 November 20th, 2010, 08:46 PM #2 Senior Member   Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs Re: Solution of y = x and y = -x If you have y = x and y = -x, you did correctly to set x = -x Add x to both sides: 2x = 0 Divide through by 2 x = 0 Think of it as +0 = -0  November 20th, 2010, 09:09 PM   #3
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Re: Solution of y = x and y = -x

Hello, bogger57!

Quote:
 I was helping someone with math and embarrassed myself today. I asked that person to use basic algebra to compute the distance between the line and the point (4,4). I told the person to: [color=beige]. . [/color] Compute the slope of all lines perpendicular to [color=beige] . [/color](We determined this was 1) [color=beige]. . [/color] Find a line with slope 1 that runs through point (4,4)[color=beige] . [/color](we determined this was the line ) [color=beige]. . [/color] Find where and intersect. [color=beige]. . [/color] Find the distance between the point of intersection and (4,4). This process went pretty well until Step #3 above, where I embarrassed myself showing the person how to solve the linear system [color=beige]. . [/color] My first instinct was to solve the system by substituting the first equation into the second equation [color=beige]. . [/color]giving:[color=beige] .[/color] But this is complete nonsense right of the bat! [color=beige] . [/color] [color=blue]No, it isn't[/color] How can ? [color=beige] . [/color] [color=blue]See my reply below.[/color] If you divide both sides by , then you get which is even more bizarre. [color=beige]. . [/color][color=blue]You must NOT divide by x . . . ever![/color] I guess I could try this:[color=beige] .[/color] [color=beige] . [/color] [color=blue]This is the correct method.[/color] But I still can't get over how can ever be .

[color=beige]. . [/color] November 27th, 2010, 07:06 PM #4 Newbie   Joined: Sep 2008 Posts: 4 Thanks: 0 Re: Solution of y = x and y = -x MarkFL and soroban: I can see how +0 = -0 so both of your answers seem to make sense to me, but I am still a little confused. Soroban says �You must NOT divide by x . . . ever!� I'm not sure what this means, since I don't remember my math teachers telling me I can't divide by x. Can someone show me what rule says I can't divide both sides of the following equations by x? yx = x x*x = x x+x+x+x=x+x+x Thanks for the Help So Far! Bogger 57 November 27th, 2010, 07:21 PM #5 Senior Member   Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs Re: Solution of y = x and y = -x Using your examples: (1) If we divide through by x: As you can see y = 1 is a solution by the multiplicative identity, i.e , however, we miss a solution, namely x = 0. A better way to solve is to subtract x from both sides: Factor. Now we get both solutions, x = 0, y = 1. (2) Just like with (1) if we divide by x, we lose the solution x = 0. (3) If we divide by x, we get no solution, however if we subtract 3x from each side, we get: In general, if we divide by f(x), we lose the solution f(x) = 0. I was actually taught that if you do divide by f(x), note f(x) = 0 as a solution, then proceed. But strictly speaking, soroban is right, you should find another way to solve, finding all solutions at the end. Tags solution Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post rain Real Analysis 1 July 17th, 2013 12:28 PM davedave Calculus 1 January 31st, 2012 02:48 PM bdcrown007 Calculus 1 January 26th, 2011 07:27 PM TreeTruffle Algebra 2 March 27th, 2010 01:22 AM leith00000 Algebra 2 August 7th, 2009 12:15 PM

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