How do you solve these 2 equatiions

Linear, quadratic, module, parametric equations

How do you solve these 2 equatiions

Postby Guest » Sat Nov 17, 2018 10:18 pm

Hi I really need your help in solving this eqns. I can't it done by myself.

Please include the steps and explanation

xy = 1/6

y+x = 5xy
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Re: How do you solve these 2 equatiions

Postby Guest » Sun Nov 18, 2018 11:29 pm

This is a system of two equations with two unknowns.
It is easy to solve by substitution.
[tex]\begin{array}{|l} x = \frac{1}{6y} (1) (we substitute) \\ x + y = 5xy \end{array}[/tex]

[tex]\frac{1}{6y}[/tex]+y=5.[tex]\frac{1}{6y}[/tex].y

[tex]\frac{1+6y^{2}}{6y}[/tex]=[tex]\frac{5}{6}[/tex]

1+6[tex]y^{2}[/tex]=5y

6[tex]y^{2}[/tex]-5y+1=0 ; y= :?:
D=25-24=1 ; [tex]y_{1,2 }[/tex]=[tex]\frac{5\pm1}{2.6}[/tex]

[tex]y_{1 }[/tex]=[tex]\frac{1}{2}[/tex] ; [tex]y_{2 }[/tex]=[tex]\frac{1}{3}[/tex] (we go back to (1))

[tex]x_{1 }[/tex]=[tex]\frac{1}{\frac{6}{2}}[/tex]=[tex]\frac{1}{3}[/tex]

[tex]x_{2 }[/tex]=[tex]\frac{1}{\frac{6}{3}}[/tex]=[tex]\frac{1}{2}[/tex]

Answer: ([tex]\frac{1}{3}[/tex];[tex]\frac{1}{2}[/tex]) , ([tex]\frac{1}{2}[/tex];[tex]\frac{1}{3}[/tex])
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