Question

Resolva os seguintes sistemas:
a) $\left \{ {{2x+3y=5} \atop {x-y=-2} \right.$
b) $\left \{ {{3x+6y=13} \atop {4x+8y=-5}} \right.$
c) $\left \{ {{2x+6y=9} \atop {-3x+5y=11}} \right.$

Answer 1

Resposta:

Vamos lá

$a)\left \{ {{2x+3y=5} \atop {x-y=-2}} \right. ||x=-2+y\\\\\\2(-2+y)+3y=5\\\\-4+2y+3y=5\\\\5y=5+4\\\\y=9/5\\\\x=-2+9/5\\\\x=-10+9/5\\\\x=-1/5\\\\\\S=\{-1/5,9/5\}$

$b)\left \{ {{3x+6y=13} \atop {4x+8y=-5}} \right. ||x=\dfrac{13-6y}{3} \\\\\\4(\dfrac{13-6y}{3} )+8y=-5\\\\\\\dfrac{52}{3} -8y+8y=-5\\\\\\0\neq 5-\dfrac{52}{3}\{inexistente\}$

$c)\left \{ {{2x+6y=9} \atop {-3x+5y=11}} \right. ||x=\dfrac{9-6y}{2} \\\\\\-3(\dfrac{9-6y}{2} )+5y=11\\\\\\-\dfrac{27}{2} +9y+5y=11\\\\\\14y=11+\dfrac{27}{2}\\\\\\14y = \dfrac{22+27}{2} \\\\\\28y=49\\\\y=\dfrac{49}{28}\\\\\\y=\dfrac{7}{4}\\\\\\\\x=\dfrac{9}{2} -3(\dfrac{7}{4})\\\\\\x=\dfrac{9}{2}-\dfrac{21}{4} \\\\\\x = \dfrac{18-21}{4} \\\\\\x =- \dfrac{3}{4} \\\\\\S=\{- \dfrac{3}{4} ,\dfrac{7}{4}\}$

║Prof Alexandre║

Universidade de Pernambuco