Question

$3x - y = 9 \\ xy = 12$
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Answer 1

-y=9-3x
y= -9+3x

xy=12

x(-9+3x)=12

-9x+3x²=12

3x²-9x-12=0

x²-3x-4=0

a=1
b=-3
c=-4

∆= b²-4ac
∆= 9-4.1.(-4)
∆= 9+16
∆=25

x= (-b±√∆)/2.1

x= (3±5)/2

x₁=(3+5)/2
x₁= 4

x₂=(3-5)/2
x₂= -2/2
x₂= -1

Quando x= 4 y= 3
y=-9+3(4)
y= -9+12
y= 3

Quando x= -1 y=-12
y=-9+3(-1)
y= -9-3
y= -12

(4,3) ou (-1,-12)