Question

$\left \{ {{3x+5y=4} \atop {7x-3y=24}} \right. \\\left \{ {{x^2-y^2=24} \atop {x-y=4}} \right.$

Answer 1

Ответ:

(3 ; –1) ;    (5 ; 1) ;

Пошаговое объяснение:

{ 3x + 5y = 4

{ 7x – 3y = 24

$\displaystyle \left \{ {{3x+5y=4 \ \ | \cdot 3} \atop {7x-3y=24 \ | \cdot 5}} \right. \Leftrightarrow \left \{ {{9x+15y=12} \atop {35x-15y=120}} \right. \bigg |+$

$9x+35x+15y-15y=12+120;$

$44x=132; \quad x=132:44; \quad x=3;$

$3x+5y=4;$

$3 \cdot 3+5y=4 \Rightarrow 5y=4-9; \quad 5y=-5; \quad y=-5:5; \quad y=-1; \quad (3; -1);$

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{ x² – y² = 24

{ x – y = 4

$\displaystyle \left \{ {{x^{2}-y^{2}=24} \atop {x-y=4}} \right. \Leftrightarrow \left \{ {{(x-y)(x+y)=24} \atop {x-y=4}} \right. \Leftrightarrow \left \{ {{4(x+y)=24} \atop {x-y=4}} \right. \Leftrightarrow \left \{ {{x+y=24:4} \atop {x-y=4}} \right. \Leftrightarrow$

$\displaystyle \Leftrightarrow \left \{ {{x+y=6} \atop {x-y=4}} \right. \bigg |+$

$x+x+y-y=6+4;$

$2x=10; \quad x=10:2; \quad x=5;$

$x-y=4 \Rightarrow 5-y=4; \quad y=5-4; \quad y=1; \quad (5; 1);$