Question

Determine, em cada item, o ponto de interseção das retas dadas:
A)y=3x+9 e y=5-6x
B)x+y=2 e x-y=8
C)2x+3y=1 e 3x-2y=4
D)x-2y+4=0 e x+y-2=0

Answer 1

a)$\left \{ {{y=3x+9} \atop {y=5-6x}} \right.$

$\left \{ {{y-3x=9 (-1)} \atop {y+6x=5}} \right.$

$\left \{ {{-y+3x=-9} \atop {y+6y=5}} \right$

9x= -4
x= -4/9

y= 3(-4/9)+9
y= -12/9+9
y= -12+81/9
y= 69/9

b) $\left \{ {{x+y=2} \atop {x-y=8}} \right.$

2x=10
x=5

5+y=2
y=2-5
y=-3

c) $\left \{ {{2x+3y=1 (2)} \atop {3x-2y=4 (3)}} \right.$

13x= 14
x=14/13

2(14/13)+3y+1
28/13+3y=1
3y=1-28/13
39y=-15
y=-5/13

d) $\left \{ {{x+2y=-4(-1)} \atop {x+y=2}} \right.$

-y=6 (-1)
y=-6

x+2(-6)=-4
x-12=-4
x= -4+12
x=8