Question

sistemas de equações:

1) x + 3y = 10
2x - y = 6


2) 2x + 3y = 29
x - y = 2


3) x + y = 12
3x - 2y = 21


4) x + 5y = 8
2x - y = 5


5) x + 4y = 15
3x - y = 19

Answer 1

Resposta:

$1:\ x=4\ e\ y=2\\\\2:\ x=7\ e\ y=5\\\\3:\ x=9\ e\ y=3\\\\4:\ x=3\ e\ y=1\\\\5:\ x=7\ e\ y=2$

Explicação passo a passo:

$1)\ \left\{\begin{array}{ccc}x+3y=10\ (i)\\2x-y=6\ (ii)\end{array}\right\\\\\\x=10-3y\ (iii)\\\\Substituido\ (iii)\ em\ (ii)\ temos:\\\\2\bullet(10-3y)-y=6\\\\20-6y-y=6\\\\-7y=6-20\\\\-7y=-14\\\\-y=-\frac{14}{7}\\\\-y=-2\\\\y=2\\\\Substituindo\ o\ valor\ de\ y\ em\ (i),\ obtemos\ o\ valor\ de\ x:\\\\x=10-3\bullet2\\\\x=10-6\\\\x=4$

$2)\ \left\{\begin{array}{ccc}2x+3y=29\ (i)\\x-y=2\ (ii)\end{array}\right\\\\\\x=\frac{29-3y}{2}\ (iii)\\\\Substituido\ (iii)\ em\ (ii)\ temos:\\\\\frac{29-3y}{2}-y=2\\\\2\bullet(\frac{29-3y}{2}-y)=2\bullet2\\\\29-3y-2y=4\\\\-5y=4-29\\\\-5y=-25\\\\-y=-\frac{25}{5}\\\\-y=-5\\\\y=5\\\\\\Substituindo\ o\ valor\ de\ y\ em\ (i),\ obtemos\ o\ valor\ de\ x:\\\\x=\frac{29-3\bullet(5)}{2}\\\\x=\frac{29-15}{2}\\\\x=\frac{14}{2}\\\\x=7$

$3)\ \left\{\begin{array}{ccc}x+y=12\ (i)\\3x-2y=21\ (ii)\end{array}\right\\\\\\x=12-y\ (iii)\\\\Substituindo\ (iii)\ em\ (ii)\ temos:\\\\3\bullet(12-y)-2y=21\\\\36-3y-2y=21\\\\-5y=21-36\\\\-5y=-15\\\\-y=-\frac{15}{5}\\\\-y=-3\\\\y=3\\\\Substituindo\ o\ valor\ de\ y\ em\ (i),\ obtemos\ o\ valor\ de\ x:\\\\x=12-3\\\\x=9$

$4)\ \left\{\begin{array}{ccc}x+5y=8\ (i)\\2x-y=5\ (ii)\end{array}\right\\\\\\x=8-5y\ (iii)\\\\Substituindo\ (iii)\ em\ (ii)\ temos:\\\\2\bullet(8-5y)-y=5\\\\16-10y-y=5\\\\-11y=5-16\\\\-11y=-11\\\\-y=-\frac{11}{11}\\\\-y=-1\\\\y=1\\\\Substituindo\ o\ valor\ de\ y\ em\ (i),\ obtemos\ o\ valor\ de\ x:\\\\x=8-5(1)\\\\x=8-5\\\\x=3$

$5)\ \left\{\begin{array}{ccc}x+4y=15\ (i)\\3x-y=19\ (ii)\end{array}\right\\\\\\x=15-4y\ (iii)\\\\Substituindo\ (iii)\ em\ (ii)\ temos:\\\\3\bullet(15-4y)-y=19\\\\45-12y-y=19\\\\-13y=19-45\\\\-13y=-26\\\\-y=-\frac{26}{13}\\\\-y=-2\\\\y=2\\\\Substituindo\ o\ valor\ de\ y\ em\ (i),\ obtemos\ o\ valor\ de\ x:\\\\x=15-4\bullet2\\\\x=15-8\\\\x=7$