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: $\displaystyle mx+2y1=0$ $\displaystyle 2x+my+3=0$ $\displaystyle xy3=0$ One of the many things I tried was to write all three in slopeintercept form like this: $\displaystyle y=(1mx)/2$ $\displaystyle y=(32x)/m$ $\displaystyle y=x3$ 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: $\displaystyle (32x)/m=x3$ $\displaystyle 32x=mx3$ $\displaystyle mx+2x=0$ $\displaystyle x(m+2)=0$ $\displaystyle x=0\text{ and }m = 2$ 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. 
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Thanks for pointing out my mistake, didn't realize I forgot how to multiply. That aside, I'm still stuck here: $\displaystyle (1−mx)/2=2x6 => x=(2+m)/7$ (equating the first and third equations and solving for x) $\displaystyle (3x3)/(m2)=(2+m)/7$ $\displaystyle (3x3)(2+m)=7(m2)$ $\displaystyle 3m^(2)+3m6=7m14 $ $\displaystyle 3m^(2)4m+8=0$ And here I can already see that this is wrong since the discriminant is negative (and m has to be a real number) $\displaystyle D=(4)^(2)4*3*8=1696=80$ 
$1  mx = 2y = 2(x  3) = 2x  6$ 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 $m = 10/3$. 
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. 
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$\left\{m= \dfrac{10}{3},x= \dfrac{21}{16},y= \dfrac{27}{16}\right\}$ option or not $m=\dfrac{10}{3}$ is the answer. 
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). 
What options were given? 
They were: 4/5,1/3,4/3,3/4 
Perhaps the 1/3 option was a typo for 10/3. Is the problem from a textbook? If so, what book? 
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