Question

URGENT!!! Se dau sistemele
1. {4|x|-y=3
{-5|x|+3y=5
2.{4x+3|y|=1
{5x+4|y|=2

Answer 1

Răspuns:

|x|= $\left \{ {{x; x\geq0} \atop {-x; x<0}} \right.$⇒

x≥0

$\left \{ {{4x-y=3} \atop {-5x+3y=5}} \right.$   ⇒ y=4x-3

-5x+3(4x-3)=5    

-5x+12x-9=5

7x=14 ⇒ x=2; y=5

x<0

$\left \{ {{-4x-y=3} \atop {5x+3y=5}} \right.$

⇒ y=-4x-3

5x+3(-4x-3)=5    

5x-12x-9=5

-7x=14 ⇒ x=-2; y=5

|y|=$\left \{ {{y; y\geq0} \atop {-y; y<0}} \right.$

x≥0

$\left \{ {{4x+3y=1 /*(-5)} \atop {5x+4y=2/*4}} \right.$

$\left \{ {{-20x-15y=-5 \atop {20x+16y=8}} \right.$ |+

   /       y=3     4x+9=1   4x=-8 ⇒ x=-2

x<0

$\left \{ {{4x-3y=1 /*(5)} \atop {5x-4y=2/*(-4)}} \right.$

$\left \{ {{20x-15y=5 } \atop {-20x+16y=-8}} \right.$ |+

   /       y=-3     4x+9=1   4x=-8 ⇒ x=-2

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