Question

rezolvati prin metoda reducerii
x+y+2=0
x-y-4+0

Answer 1

$\left \{ {{x+y+2=0} \atop {x-y-4=0}} \right.$⇔
$\left \{ {{x+y=-2} \atop {x-y=4}} \right.$
Adunand membru cu membru cele doua ecuatii ale sistemului avem ca:
$x+y+x-y=-2+4$⇔
$2x=2$⇒$x= \frac{2}{2}$⇒$x=1$
$\left \{ {{x+y=-2} \atop {x=1}} \right.$⇒$\left \{ {{1+y=-2} \atop {x=1}} \right.$⇔$\left \{ {{y=-2-1} \atop {x=1}} \right.$⇒$y=-3$
Solutia sitemului este:
$S=\{1, -3\}$