Question

Решите систему уравнений
а) y-2x=1
6x-y=7
б) 7x-3y=13
x-2y=5​

Answer 1

Ответ:

$1)~~(2,\, 5)\\2)~~(1,\, -2)$

Объяснение:

$1)~~\displaystyle \left \{ {{y-2x=1} \atop {6x-y=7}} \right.$

Сложим строки системы

$\displaystyle \left \{ {{y-2x=1} \atop {6x-y+y-2x=7+1}} \right.\\\\\left \{ {{y-2x=1} \atop {6x-y+y-2x=7+1}} \right.\\\\\left \{ {{y-2x=1} \atop {4x=8}} \right.\\\\\left \{ {{y-2\cdot 2=1} \atop {x=2}} \right.\\\\\left \{ {{y=5} \atop {x=2}} \right.$

$2)~~\displaystyle \left \{ {{7x-3y=13} \atop {x-2y=5}} \right.$

Выразим $x$ через $y$

$\displaystyle \left \{ {{7x-3y=13} \atop {x=2y+5}} \right.\\\\\left \{ {{7\cdot(2y+5)-3y=13} \atop {x=2y+5}} \right.\\\\\left \{ {{14y+35-3y=13} \atop {x=2y+5}} \right.\\\\\left \{ {{11y=13-35} \atop {x=2y+5}} \right.\\\\\left \{ {{11y=-22} \atop {x=2y+5}} \right.\\\\\left \{ {{y=-2} \atop {x=2\cdot(-2)+5}} \right.\\\\\left \{ {{y=-2} \atop {x=1}} \right.$