Question

x+2/4 + y-1/2 = 7/2 x-5/2 - x-3/3 = 1/6 metodo de igualación

Answer 1

X+2/4 + y-1/2 = 7/2 x-5/2 - y -3/3 = 1/6 metodo de igualación

$========================================$

$\textbf{M\'etodo de Igualaci\'on.}\\ \\ Vamos\ a\ despejar\ "x". \\ \\ Ecua(1) : \\ \\ x + \dfrac{2}{4}+y -\dfrac{1}{2} = \dfrac{7}{2} \\ \\ El\ mcm\ de\ los\ denominadores\ es\ "4". \\ \\ x + \dfrac{2}{4}+y -\dfrac{1*2}{2*2} = \dfrac{7*2}{2*2} \\ \\ \\ x + \not{\dfrac{2}{4}}+y -\not{\dfrac{2}{4}} = \dfrac{14}{4} \\ \\ \\ x = \dfrac{14:2}{4:2}-y \\ \\ \\ \boxed{x = \frac{7}{2}-y }$

$===============================$

$Ecua(2) : \\ \\ Despejamos\ "x". \\ \\ x- \dfrac{5}{2}-y-\dfrac{3}{3} = \dfrac{1}{6} \\ \\ \\ x- \dfrac{5*3}{2*3}-y-\dfrac{3*2}{3*2} = \dfrac{1}{6} \\ \\ \\ x- \dfrac{15}{6}-y-\dfrac{6}{6} = \dfrac{1}{6} \\ \\ \\ x = \dfrac{1}{6}+ \dfrac{15}{6}+ \dfrac{6}{6}+y \\ \\ \\ x = \dfrac{22:2}{6:2}+y \\ \\ \\ \boxed{\boxed{x= \frac{11}{3}+y }}$

$=====================================$

$Ahora\ igualamos. \\ \\ Ecua(1) = Ecua(2) .$

$\dfrac{7}{2} -y = \dfrac{22}{6} + y \\ \\ \\ \dfrac{21}{6} - \dfrac{22}{6} = 2y \\ \\ \\ - \dfrac{1}{6} = 2y \\ \\ \\ \boxed{\boxed{- \frac{1}{12} =y}}$

Ahora reemplazamos en cualquiera de las ecuaciones en "y", para hallar el valor de "x".

Reemplazamos en la Ecua(2).

$x = \dfrac{22}{6} + y \\ \\ \\ x = \dfrac{44}{12} - \dfrac{1}{12} \\ \\ \\ \boxed{\boxed{x= \frac{43}{12} }}$