# How do you solve these 2 equatiions

Linear, quadratic, module, parametric equations

### How do you solve these 2 equatiions

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

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

$$\frac{1}{6y}$$+y=5.$$\frac{1}{6y}$$.y

$$\frac{1+6y^{2}}{6y}$$=$$\frac{5}{6}$$

1+6$$y^{2}$$=5y

6$$y^{2}$$-5y+1=0 ; y=
D=25-24=1 ; $$y_{1,2 }$$=$$\frac{5\pm1}{2.6}$$

$$y_{1 }$$=$$\frac{1}{2}$$ ; $$y_{2 }$$=$$\frac{1}{3}$$ (we go back to (1))

$$x_{1 }$$=$$\frac{1}{\frac{6}{2}}$$=$$\frac{1}{3}$$

$$x_{2 }$$=$$\frac{1}{\frac{6}{3}}$$=$$\frac{1}{2}$$

Answer: ($$\frac{1}{3}$$;$$\frac{1}{2}$$) , ($$\frac{1}{2}$$;$$\frac{1}{3}$$)
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