Question

реши систему уравнений:
2x-y=12
x-3y=15

Answer 1

Объяснение:

{2х-у=12

{х=15+3у

{2(15+3у)-у=12

{х=15+3у

{30+6у-у=12

{х=15+3у

{3у=-18

{х=15+3у

{у=-6

{х=-3

Answer 2

Ответ:

$\displaystyle \left \{ {{y=-\dfrac{18}{5}} \atop {x=\dfrac{21}5}} \right.$

Объяснение:

$\displaystyle \left \{ {{2x-y=12} \atop {x-3y=15}} \right.$

Выразим $y$ через $x$ в первом уравнении и подставим во второе

$\displaystyle \left \{ {{y=2x-12} \atop {x-3\cdot(2x-12)=15}} \right.\Bigg.\\\\\left \{ {{y=2x-12} \atop {x-6x+36=15}} \right.\Bigg.\\\\\left \{ {{y=2x-12} \atop {-5x+36=15}} \right.\Bigg.\\\\\left \{ {{y=2x-12} \atop {-5x=-21}} \right.\Bigg.\\\\\left \{ {{y=2x-12} \atop {x=\dfrac{21}5}} \right.\Bigg.\\\\\\\left \{ {{y=2\cdot\dfrac{21}5-12} \atop {x=\dfrac{21}5}} \right.\Bigg.\\\\\left \{ {{y=-\dfrac{18}{5} \atop {x=\dfrac{21}5}} \right.\Bigg.$