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yaroslaw [1]
3 years ago
8

Is 2.0 a solution to the equation? X-2y=0 , 2x-3y=1

Mathematics
1 answer:
Travka [436]3 years ago
8 0
No, because (2,0) is a coordinate. x=2 and y=0. So just plug in the numbers where there's x or y with the appropriate number, (2 or 0). So in the first equation, x-2y=0, when you pug in the numbers, 2-2(0)=0, you know it's wrong because 2-0=0 isn't correct. So no. the point (2,0) is not a solution to the first equation. Now plug in the numbers for the second coordinate. You get 2(2)-3(0)=1. So 4-0=1. This is once again false no no. (2,0) satisfies neither equations. 
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Step-by-step explanation:

Given bi-quadratic equation is:

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Substituting x^2=a, given bi-quadratic equation reduces in the form of following quadratic equation:

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Let us factorize the above quadratic equation:

a^2 +95a -500=0\\\therefore\: a^2 +100a -5a-500=0\\\therefore\: a(a +100) -5(a+100)=0\\\therefore\: (a +100)(a -5)=0\\\therefore\: (a +100)=0\:\: or \:\: (a -5)=0\\\therefore\: a = - 100\:\: or \:\: a = 5\\\\CASE\: (1)\:\\When\: a = - 100 \implies x^2 = - 100\\\therefore x=\pm \sqrt{-100}\\

Since square root of a negative number cannot be found, so:

x \neq \pm \sqrt{-100}\\

CASE\: (2)\:\\When\: a =5 \implies x^2 =5\\\therefore x=\pm \sqrt{5}\\

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