Question

Resuelve el metodo de igualasion de los sguientes sistemas de ecuacion
2x+3y=2
-6x+12y=1
x+y=4x
x-y=2
x+3=1
x+y=9
2x+3y=1
-x+y=1

Answer 1

$\textbf{Resolvemos:}\\\\\begin{cases}&\mathrm{2x+3y=1}\quad\Longrightarrow Ecuaci\'on\ 1\\&\mathrm{-x+y=1}\quad\Longrightarrow Ecuaci\'on\ 2\end{cases}\\\\\\\textbf{Despejamos "y" en la ecuaci\'on 1:}\\\\\mathrm{y=\dfrac{1-2x}{3}}\\\\\textbf{Despejamos "y" en la ecuaci\'on 2:}\\\\\mathrm{y=1+x}\\\\\textbf{Igualamos la ecuaci\'on 1 y 2:}\\\\\mathrm{\dfrac{1-2x}{3}=1+x}\\\\\\\mathrm{3\left(\dfrac{1-2x}{3}=1+x\right)}\\\\\\\mathrm{1-2x=3+3x\right)}\\\\\\\mathrm{-2x-3x=3-1\right)}$

$\mathrm{-5x=2\right)}\\\\\\\mathbf{x=-\dfrac{2}{5}\right)}\quad\Longrightarrow\ \boxed{Valor\ de\ "x"}$

$\textbf{Reemplazamos "x" en la ecuaci\'on 2:}\\\\\mathrm{-\left(-\dfrac{2}{5}\right)+y=1}\\\\\\\mathrm{5\left(\dfrac{2}{5}+y=1\right)}\\\\\\\mathrm{2+5y=5}\\\\\\\mathrm{5y=5-2}\\\\\\\mathrm{5y=3}\\\\\\\mathbf{y=\dfrac{3}{5}}\quad\Longrightarrow\boxed{Valor\ de\ "y"}\\\\\\\textbf{RESPUESTAS:}\\\\\boxed{\boxed{\mathbf{x=-\dfrac{2}{5}\ \ ;\ \ y=\dfrac{3}{5}}}}$