Question

Помогите решить линейные уравнения способом подстановки

Answer 1

Ответ: а) х=1, у=4; б) x=5, y=5; в) x=1, y=0.

Объяснение:

а) $\left \{ {{x+y=5} \atop {3x+y=7}} \right.$

$\left \{ {{x=5-y} \atop {3(5-y)+y=7}} \right.$

$\left \{ {{x=5-y \atop {15-3y+y=7}} \right.$

$\left \{ {{x=5-y} \atop {-2y=-8}} \right.$

$\left \{ {{x=5-4=1} \atop {y=4}} \right.$.

б) $\left \{ {{3x-2y=5} \atop {x+2y=15}} \right.$

$\left \{ {{3(15-2y)-2y=5} \atop {x=15-2y}} \right.$

$\left \{ {{45-6y-2y=5} \atop {x=15-2y}} \right.$

$\left \{ {{-8y=-40} \atop {x=15-2y}} \right.$

$\left \{ {{y=5} \atop {x=15-2*5}} \right.$

$\left \{ {{y=5} \atop {x=5}} \right.$

в) $\left \{ {{2x-y=2} \atop {3x-2y=3}} \right.$

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

$\left \{ {{x=(2+y)/2} \atop {(6+3y)/2-2y=3}} \right.$

$\left \{ {{x=(2+y)/2} \atop {6+3y-4y=6}} \right.$

$\left \{ {{x=(2+y)/2} \atop {-y=0}} \right.$

$\left \{ {{x=(2+0)/2=1} \atop {y=0}} \right.$