Question

Como resolver 2x+y=1, -2x+3y=19

Answer 1

SOLUCIÓN

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                                $Despejaremos\:"x"\:de\:la\:primera\:ecuaci\'on\\\\2x+y=1\\\\\\2x=1-y\\\\\\x=\dfrac{1-y}{2}\\\\\\Reemplazamos\:x\:en\:la\:segunda\:ecuaci\'on\\\\\\-2x+3y=19\\\\\\(-2)\left(\dfrac{1-y}{2}\right)+3y=19\\\\\\\dfrac{(-2)(1-y)+[(2)(3y)]}{2}=19\\\\\\(-2+2y)+(6y)=(19)(2)\\\\\\-2+8y=38\\\\\\8y=40\\\\\\y=\dfrac{40}{8}\\\\\\\boxed{\boldsymbol{y=5}}$

                                $Reemplazamos\:"y"\:en\:"x"\\\\\\x=\dfrac{1-1y}{2}\\\\\\x=\dfrac{1-(5)}{2}\\\\\\x=\dfrac{1-5}{2}\\\\\\x=\dfrac{-4}{2}\\\\\\\boxed{\boldsymbol{x=-2}}$