Question

Resolva os sistemas.
a) {x + 5y=3
2x+ 3y=13

b) {5x + 3y=11
6x – y=4

c) {3x –2y=1
4x +5y=2

d) {8x –4y –2=1–y
3x –2=2y + 6x

Answer 1

a)

$\left \{ {{x+5y=3} \atop {2x+3y=13}} \right. \\ \\ \frac{13-3y}{2}+5y=3 \\ 13+7y=6 \\ y= \frac{-7}{7}=-1 \\ x + 5(-1)=3 \\ x=3+5=8 \\ \\ \left \{ {{y=-1} \atop {x=8}} \right.$

b)

$\left \{ {{5x+3y=11} \atop {6x-y=4}} \right. \\ \\ 5x+3(6x-4)=11 \\ 5x+18x-12=11 \\ 23x=23 \ | \ x=1 \\ 6(1)-y=4 \\ -y=-2 \ | \ y=2 \\ \\ \left \{ {{y=2} \atop {x=1}} \right.$

c)

$\left \{ {{3x-2y=1} \atop {4x+5y=2}} \right. \\ \\ 3x-2( \frac{2-4x}{5})=1 \\ \frac{15x-4+8x}{5}=1 \\ 23x=9 \ | \ x= \frac{9}{23} \\ 3( \frac{9}{23})-2y=1 \\ 27-46y=23 \\ y= \frac{4}{46} \ | \ y= \frac{2}{23} \\ \\ \left \{ {{y=2/23} \atop {x=9/23}} \right.$

d)

$\left \{ {{8x-3y=3} \atop {2y+3x=-2}} \right. \\ \\ 8[ \frac{-2(1+y)}{3}]-3y=3 \\ -16-16y-9y=9 \\ -25y=25 \ | \ y=-1 \\ 2(-1)+3x=-2 \\ 3x=0 \ | \ x=0 \\ \\ \left \{ {{y=-1} \atop {x=0}} \right.$