 My Math Forum Intersection of three lines - aka a system of three equations with three variables
 User Name Remember Me? Password

 Algebra Pre-Algebra and Basic Algebra Math Forum

 July 6th, 2019, 05:35 AM #1 Newbie   Joined: Feb 2017 From: Peja Posts: 11 Thanks: 0 Math Focus: Jack of all trades, master of none, though often better, than master of one. Intersection of three lines - aka a system of three equations with three variables So I'm supposed to find the value of m for which these three lines intersect at the same point: $\displaystyle mx+2y-1=0$ $\displaystyle 2x+my+3=0$ $\displaystyle x-y-3=0$ One of the many things I tried was to write all three in slope-intercept form like this: $\displaystyle y=(1-mx)/2$ $\displaystyle y=(-3-2x)/m$ $\displaystyle y=x-3$ Then I thought, I can just equate the second and third equation since I know for sure that the lines do intersect, and that left me with this mess: $\displaystyle (-3-2x)/m=x-3$ $\displaystyle -3-2x=mx-3$ $\displaystyle mx+2x=0$ $\displaystyle x(m+2)=0$ $\displaystyle x=0\text{ and }m = -2$ Now I'm pretty damn sure that this is not the solution, in fact I'm convinced that my whole method of going into this is wrong. Last edited by skipjack; July 6th, 2019 at 07:42 AM. July 6th, 2019, 06:42 AM   #2
Member

Joined: Oct 2018
From: USA

Posts: 89
Thanks: 61

Math Focus: Algebraic Geometry
Quote:
 Originally Posted by granitba $\displaystyle (-3-2x)/m=x-3$ $\displaystyle -3-2x=mx-3$
Should be $3-2x = mx -3m$ since you have to distribute. Maybe this can push you in the right direction. July 6th, 2019, 08:31 AM #3 Newbie   Joined: Feb 2017 From: Peja Posts: 11 Thanks: 0 Math Focus: Jack of all trades, master of none, though often better, than master of one. Thanks for pointing out my mistake, didn't realize I forgot how to multiply. That aside, I'm still stuck here: $\displaystyle (1−mx)/2=2x-6 => x=(2+m)/7$ (equating the first and third equations and solving for x) $\displaystyle (3x-3)/(m-2)=(2+m)/7$ $\displaystyle (3x-3)(2+m)=7(m-2)$ $\displaystyle 3m^(2)+3m-6=7m-14$ $\displaystyle 3m^(2)-4m+8=0$ And here I can already see that this is wrong since the discriminant is negative (and m has to be a real number) $\displaystyle D=(-4)^(2)-4*3*8=16-96=-80$ Last edited by skipjack; July 6th, 2019 at 09:43 AM. July 6th, 2019, 10:00 AM #4 Global Moderator   Joined: Dec 2006 Posts: 20,965 Thanks: 2214 $1 - mx = 2y = 2(x - 3) = 2x - 6$ implies $(m + 2)x = 7$. The first two equations imply $(m + 2)x + (m + 2)y + 2 = 0$, so $(m + 2)x + (m + 2)(x - 3) + 2 = 0$. Hence $7 + 7 - 3(m + 2) + 2 = 0$, which leads to $m = 10/3$. Thanks from granitba July 7th, 2019, 10:51 AM #5 Newbie   Joined: Feb 2017 From: Peja Posts: 11 Thanks: 0 Math Focus: Jack of all trades, master of none, though often better, than master of one. Oh, that's one of the many ways I tried to solve it, and I also got 10/3. Problem is, 10/3 is not an option. July 7th, 2019, 11:16 AM   #6
Senior Member

Joined: Sep 2015
From: USA

Posts: 2,549
Thanks: 1399

Quote:
 Originally Posted by granitba Oh, that's one of the many ways I tried to solve it, and I also got 10/3. Problem is, 10/3 is not an option.
I'm showing one solution

$\left\{m= \dfrac{10}{3},x= \dfrac{21}{16},y= -\dfrac{27}{16}\right\}$

option or not $m=\dfrac{10}{3}$ is the answer. July 7th, 2019, 12:37 PM #7 Newbie   Joined: Feb 2017 From: Peja Posts: 11 Thanks: 0 Math Focus: Jack of all trades, master of none, though often better, than master of one. Thanks for the input, I guess the authors got it wrong, even WolframAlpha shows 10/3 to be the result (I thought it was some input error on my side). July 7th, 2019, 06:00 PM #8 Global Moderator   Joined: Dec 2006 Posts: 20,965 Thanks: 2214 What options were given? July 8th, 2019, 02:37 AM #9 Newbie   Joined: Feb 2017 From: Peja Posts: 11 Thanks: 0 Math Focus: Jack of all trades, master of none, though often better, than master of one. They were: -4/5,1/3,-4/3,3/4 July 8th, 2019, 07:23 AM #10 Global Moderator   Joined: Dec 2006 Posts: 20,965 Thanks: 2214 Perhaps the 1/3 option was a typo for 10/3. Is the problem from a textbook? If so, what book? Tags aka, equations, intersection, linear equation, lines, system, variables 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 TylerD007 Elementary Math 1 December 20th, 2015 01:40 PM matej Elementary Math 5 February 8th, 2015 11:46 AM Monox D. I-Fly Elementary Math 4 August 21st, 2014 06:42 AM nicnicman Linear Algebra 4 October 22nd, 2013 02:27 AM 500lbgorilla Algebra 4 January 24th, 2009 07:59 AM

 Contact - Home - Forums - Cryptocurrency Forum - Top      