Question

|x-y|=2
|x|+|y| = 4
Решите систему

Answer 1

$left { {{|x-y|=2} atop {|x|+|y|=4}} right. to left { {{ left[begin{array}{ccc}x-y=2\-x+y=2end{array}right} atop {|x|+|y|=4}} right. \ \ left { {{x-y=2} atop {|x|+|y|=4}} right. to left { {{x=y+2} atop {|y+2|+|y|=4}} right. \ \ left { {{y geq 0} atop {y+2 geq 0}}atop {y+2+y=4} right. \ 2y=2 \ y=1 \ x=3$

$left { {{y<0} atop {y+2 geq 0}} right. \ y+2-y=4 \ 0=2 \ x=O \ \ left { {{y<0} atop {y+2<0}} right. \ -y-2-y=4 \ -2y=2 \ y=-1 \ x=-3$

Теперь второе

$left { {{-x+y=2} atop {|x|+|y|=4}} right. to left { {{x=y-2} atop {|y-2|+|y|=4}} right. \ left { {{y geq 0} atop {y -2geq 0}} right. \ y-2+y=4 \ 2y=6 \ y=3; \ x=1$

$left { {{y<0} atop {y-2<0}} right. \ -y+2-y=4 \ -2y=2 \ y=-1 \ x=-3 \ \ \ \ OTBET:(3;1),(-1;-3),(1;3),(-3;-1).$

Answer 2

/x-y/=2
/x/+/y/=4
x-y=2 или х-у=-2
х=2+у  или х=y-2
1)х=у+2
/2+y/+/y/=4
a)y<-2
-2-y-y=4
-2y=6
y=-3⇒x=2-3=-1
б)-2≤y≤0
2+y-y=4
Нет решения
в)y>0
2+y+y=4
2y=2
y=1⇒x=1+2=3
2)х=у-2
/у-2/+/у/=4
а)у<0
2-y-y=4
2y=-2
y=-1⇒x=-1-2=-3
б)0≤y≤2
2-y+y=4
Нет решения
в)y>2
y-2+y=4
2y=6
y=3⇒x=3-2=1

Ответ (-1;-3),(1;3),(-3;-1),(1;3)