Question

Resolva os sistemas a seguir pelo método da adição:

Answer 1

e) $\left \{ {{ \frac{x+y}{7}= \frac{2}{13}(2x-y)} \atop {x+y=14}} \right.$
$y=14-x$    $\frac{x+14-x}{7} = \frac{4x-2(14-x)}{13} \\ 2= \frac{4x-28+2x}{13} \\ 26=6x-28 \\ 6x=54 \\ x= \frac{54}{6} \\ x= 9$    $y=14-9 \\ y=5$

f) $\left \{ {{2(x-5)=7(3-y)} \atop { \frac{x-y}{3}- \frac{x+y}{4} = \frac{-37}{12} }} \right.$
$2x-10=21-7y \\ 2x=31-7y \\ x= \frac{31-7y}{2}$    $\frac{ \frac{31-7y}{2}-y }{3} - \frac{ \frac{31-7y}{2}+y }{4} =- \frac{37}{12} \\ 4( \frac{31-7y}{2} -y)-3( \frac{31-7y}{2}+y)=-37 \\ 124-28y-8y-93+21y-6y=-74 \\ -21y+31=-74 \\ 21y=105 \\ y= \frac{105}{21} \\ y=5$    $x= \frac{31-7(5)}{2} \\ x= \frac{31-35}{2} \\ x= \frac{-4}{2} \\ x=-2$