Question

Решите систему линейных уравнений: а) a+b=6 5a-2b=9 б) x+2y=5 x+3y=7

Answer 1

Объяснение:

$\tt\displaystyle\left \{{{a+b=6} \atop {5a-2b=9}} \right.\left \{ {{a=6-b} \atop {5a-2b=9}} \right.\left \{ {{a=6-b} \atop {5(6-b)-2b=9}} \right.\left \{ {{a=6-b} \atop {30-5b-2b=9}} \right. \left \{ {{a=6-b \atop {30-7b=9}} \right.$

30 - 7b = 9

7b = 30 - 9

7b = 21

b = 21 : 7

b = 3

a = 6 - b = 6 - 3

a = 3

ответ: a = 3, b = 3.

$\tt\displaystyle\left \{ {{x+2y=5} \atop {x+3y=7}} \right.\left \{ {{x=5-2y} \atop {x+3y=7}} \right.\left \{ {{x=5-2y} \atop {5-2y+3y=7}} \right.\left \{ {{x=5-2y} \atop {5+y=7}} \right.\left \{ {{x=5-2y} \atop {y=7-5}} \right.\left \{ {{x=5-2*2} \atop {y=2}} \right. \\\\\\\left \{ {{x=5-4} \atop {y=2}} \right. \left \{ {{x=1} \atop {y=2}} \right.$

ответ: x = 1, y = 2.