Алгебра 7 класс контрольные работы Виленкин ответы – страница 54

а) $$ \left\{\begin{array}{c} x+y=3 \\ 4 x-3 y=-16 \end{array}\right. $$ ⇒ $$ \left\{\begin{array}{c} x=3-y \\ 4 x-3 y=-16 \end{array}\right. $$ ⇒ $$ \left\{\begin{array}{c} x=3-y \\ 4(3-y) - 3y=-16 \end{array}\right. $$ ⇒ $$ \left\{\begin{array}{c} x=3-y \\ 12 - 4y - 3y=-16 \end{array}\right. $$ ⇒ $$ \left\{\begin{array}{c} x=3-y \\ 12 - 7y=-16 \end{array}\right. $$ ⇒ $$ \left\{\begin{array}{c} x=3-y \\ 7y=16 +12 \end{array}\right. $$ ⇒ $$ \left\{\begin{array}{c} x=3-y \\ 7y=28 \end{array}\right. $$ ⇒ $$ \left\{\begin{array}{c} x=3-y \\ y=4 \end{array}\right. $$ ⇒ $$ \left\{\begin{array}{c} x=3-4 \\ y=4 \end{array}\right. $$ ⇒ $$ \left\{\begin{array}{c} x=-1 \\ y=4 \end{array}\right. $$
    Ответ: (– 1; 4)
б) $$ \left\{\begin{array}{c} x-3 y=8 \\ 2 x+5 y=5 \end{array}\right. $$ ⇒ $$ \left\{\begin{array}{c} x=3 y +8 \\ 2 x+5 y=5 \end{array}\right. $$ ⇒ $$ \left\{\begin{array}{c} x=3 y +8 \\ 2(3y + 8) +5y=5 \end{array}\right. $$ ⇒ $$ \left\{\begin{array}{c} x=3 y +8 \\ 6y + 16 +5y=5 \end{array}\right. $$ ⇒ $$ \left\{\begin{array}{c} x=3 y +8 \\ 11y + 16=5 \end{array}\right. $$ ⇒ $$ \left\{\begin{array}{c} x=3 y +8 \\ 11y =5 -16 \end{array}\right. $$ ⇒ $$ \left\{\begin{array}{c} x=3 y +8 \\ 11y = -11 \end{array}\right. $$ ⇒ $$ \left\{\begin{array}{c} x=3 y +8 \\ y = -1 \end{array}\right. $$ ⇒ $$ \left\{\begin{array}{c} x=3 ·(-1) +8 \\ y = -1 \end{array}\right. $$ ⇒ $$ \left\{\begin{array}{c} x=5 \\ y = -1 \end{array}\right. $$
    Ответ: (5; – 1)

$$ \left\{\begin{array}{l} 7 x-2 y=8 \\ 5 x-y=13 \end{array}\right. $$ ⇒ $$ \left\{\begin{array}{l} 7 x-2 y=8 \\ y=5 x-13 \end{array}\right. $$ ⇒ $$ \left\{\begin{array}{c} 7 x-2(5 x-13)=8 \\ y=5 x-13 \end{array}\right. $$ ⇒ $$ \left\{\begin{array}{c} 7 x-10 x-26=8 \\ y=5 x-13 \end{array}\right. $$ ⇒ $$ \left\{\begin{array}{c} 26 - 3x =8 \\ y=5 x-13 \end{array}\right. $$ ⇒ $$ \left\{\begin{array}{c} 3x =26 - 8 \\ y=5 x-13 \end{array}\right. $$ ⇒ $$ \left\{\begin{array}{c} 3x =18 \\ y=5 x-13 \end{array}\right. $$ ⇒ $$ \left\{\begin{array}{c} x =6 \\ y=5 x-13 \end{array}\right. $$ ⇒ $$ \left\{\begin{array}{c} x =6 \\ y=5·6 -13 \end{array}\right. $$ ⇒ $$ \left\{\begin{array}{c} x =6 \\ y=17 \end{array}\right. $$
(6; 17) — координаты точки пересечения графиков данных уравнений.
Ответ: (6; 17).

а) $$ \left\{\begin{array}{c} x-y=7, \\ 2 x+7 y=5; \end{array}\right. $$ ⇒ $$ \left\{\begin{array}{c} x=y+ 7, \\ 2 x+7 y=5; \end{array}\right. $$ ⇒ $$ \left\{\begin{array}{c} x=y+ 7, \\ 2(y+7) + 7 y=5; \end{array}\right. $$ ⇒ $$ \left\{\begin{array}{c} x=y+ 7, \\ 2y+14 + 7 y=5; \end{array}\right. $$ ⇒ $$ \left\{\begin{array}{c} x=y+ 7, \\ 9y+14=5; \end{array}\right. $$ ⇒ $$ \left\{\begin{array}{c} x=y+ 7, \\ 9y=5 - 14; \end{array}\right. $$ ⇒ $$ \left\{\begin{array}{c} x=y+ 7, \\ 9y=- 9; \end{array}\right. $$ ⇒ $$ \left\{\begin{array}{c} x=y+ 7, \\ y=- 1; \end{array}\right. $$ ⇒ $$ \left\{\begin{array}{c} x=- 1+ 7, \\ y=- 1; \end{array}\right. $$ ⇒ $$ \left\{\begin{array}{c} x=6, \\ y=- 1; \end{array}\right. $$
Ответ: (6; – 1)
б) $$ \left\{\begin{array}{c} x+2 y=4, \\ 3 x-5 y=-21. \end{array}\right. $$ ⇒ $$ \left\{\begin{array}{c} x=4-2 y, \\ 3 x-5 y=-21. \end{array}\right. $$ ⇒ $$ \left\{\begin{array}{c} x=4-2 y, \\ 3(4-2y) -5 y=-21. \end{array}\right. $$ ⇒ $$ \left\{\begin{array}{c} x=4-2 y, \\ 12-6y -5 y=-21. \end{array}\right. $$ ⇒ $$ \left\{\begin{array}{c} x=4-2 y, \\ 12-11y=-21. \end{array}\right. $$ ⇒ $$ \left\{\begin{array}{c} x=4-2 y, \\ 11y=12 +21. \end{array}\right. $$ ⇒ $$ \left\{\begin{array}{c} x=4-2 y, \\ 11y=33. \end{array}\right. $$ ⇒ $$ \left\{\begin{array}{c} x=4-2 y, \\ y=3. \end{array}\right. $$ ⇒ $$ \left\{\begin{array}{c} x=4-2·3, \\ y=3. \end{array}\right. $$ ⇒ $$ \left\{\begin{array}{c} x=-2, \\ y=3. \end{array}\right. $$
Ответ: (– 2; 3)

$$ \left\{\begin{array}{l} 5 x-3 y=26 \\ 4 x+y=14 \end{array}\right. $$ ⇒ $$ \left\{\begin{array}{l} 5 x-3 y=26 \\ y=14 - 4 x \end{array}\right. $$ ⇒ $$ \left\{\begin{array}{l} 5 x-3 (14-4x)=26 \\ y=14 - 4 x \end{array}\right. $$ ⇒ $$ \left\{\begin{array}{l} 5 x-42 + 12x=26 \\ y=14 - 4 x \end{array}\right. $$ ⇒ $$ \left\{\begin{array}{l} 17 x-42 =26 \\ y=14 - 4 x \end{array}\right. $$ ⇒ $$ \left\{\begin{array}{l} 17 x =26 + 42\\ y=14 - 4 x \end{array}\right. $$ ⇒ $$ \left\{\begin{array}{l} 17 x =68\\ y=14 - 4 x \end{array}\right. $$ ⇒ $$ \left\{\begin{array}{l} x =4\\ y=14 - 4 x \end{array}\right. $$ ⇒ $$ \left\{\begin{array}{l} x =4\\ y=14 - 4 ·4 \end{array}\right. $$ ⇒ $$ \left\{\begin{array}{l} x =4\\ y= - 2 \end{array}\right. $$
(4; – 2) — координаты точки пересечения графиков данных уравнений.
Ответ: (4; – 2).