1) ax - 3y = 6 содержит точку (3;-3) ⇒ а·3 - 3·(-3) = 6 ⇒ a = -1
Ответ: а=-1.
![2)\ \begin{cases} 4x+3y=2 \\ -2x+2y=6 \end{cases} \ \textless \ =\ \textgreater \ \begin{cases} 4x+3y=2 \\ -4x+4y=12 \end{cases} \ \textless \ =\ \textgreater \ \begin{cases} 7y=14 \\ y=x+3 \end{cases}\\ =\ \textgreater \ \begin{cases} y=2 \\ x=5 \end{cases} =\ \textgreater \ (5;2)](https://tex.z-dn.net/?f=2%29%5C+%5Cbegin%7Bcases%7D+4x%2B3y%3D2+%5C%5C+-2x%2B2y%3D6+%5Cend%7Bcases%7D+%5C+%5Ctextless+%5C+%3D%5C+%5Ctextgreater+%5C++%5Cbegin%7Bcases%7D+4x%2B3y%3D2+%5C%5C+-4x%2B4y%3D12+%5Cend%7Bcases%7D+%5C+%5Ctextless+%5C+%3D%5C+%5Ctextgreater+%5C++%5Cbegin%7Bcases%7D+7y%3D14+%5C%5C+y%3Dx%2B3+%5Cend%7Bcases%7D%5C%5C+%3D%5C+%5Ctextgreater+%5C++%5Cbegin%7Bcases%7D+y%3D2+%5C%5C+x%3D5+%5Cend%7Bcases%7D+%3D%5C+%5Ctextgreater+%5C++%285%3B2%29)
Ответ: (5; 2) - точка пересечения
![3)\ \begin{cases} x+y=5 \\ 3(x+y)-2(x-y)=17 \end{cases} \ \textless \ =\ \textgreater \ \begin{cases} x+y=5 \\ 15-2(x-y)=17 \end{cases} \ \textless \ =\ \textgreater \ \\ \begin{cases} x+y=5 \\ 2(x-y)=-2 \end{cases} \ \textless \ =\ \textgreater \ \begin{cases} x+y=5 \\ x-y=-1 \end{cases} \ \textless \ =\ \textgreater \ \begin{cases} 2x=4 \\ 2y=6 \end{cases} \ \textless \ =\ \textgreater \ \\ \begin{cases} x=2 \\ y=3 \end{cases}](https://tex.z-dn.net/?f=3%29%5C+%5Cbegin%7Bcases%7D+x%2By%3D5+%5C%5C+3%28x%2By%29-2%28x-y%29%3D17+%5Cend%7Bcases%7D+%5C+%5Ctextless+%5C+%3D%5C+%5Ctextgreater+%5C++%5Cbegin%7Bcases%7D+x%2By%3D5+%5C%5C+15-2%28x-y%29%3D17+%5Cend%7Bcases%7D+%5C+%5Ctextless+%5C+%3D%5C+%5Ctextgreater+%5C+%5C%5C+%5Cbegin%7Bcases%7D+x%2By%3D5+%5C%5C+2%28x-y%29%3D-2+%5Cend%7Bcases%7D+%5C+%5Ctextless+%5C+%3D%5C+%5Ctextgreater+%5C++%5Cbegin%7Bcases%7D+x%2By%3D5+%5C%5C+x-y%3D-1+%5Cend%7Bcases%7D+%5C+%5Ctextless+%5C+%3D%5C+%5Ctextgreater+%5C++%5Cbegin%7Bcases%7D+2x%3D4+%5C%5C+2y%3D6+%5Cend%7Bcases%7D+%5C+%5Ctextless+%5C+%3D%5C+%5Ctextgreater+%5C++%5C%5C+%5Cbegin%7Bcases%7D+x%3D2+%5C%5C+y%3D3+%5Cend%7Bcases%7D)
Ответ: (2; 3).
![4)\ \begin{cases} ax+3y=5 \\ 12x+9y=15 \end{cases} \ \textless \ =\ \textgreater \ \begin{cases} ax+3y=5 \\ 4x+3y=5 \end{cases}](https://tex.z-dn.net/?f=4%29%5C+%5Cbegin%7Bcases%7D+ax%2B3y%3D5+%5C%5C+12x%2B9y%3D15+%5Cend%7Bcases%7D+%5C+%5Ctextless+%5C+%3D%5C+%5Ctextgreater+%5C++%5Cbegin%7Bcases%7D+ax%2B3y%3D5+%5C%5C+4x%2B3y%3D5+%5Cend%7Bcases%7D)
Система имеет бесконечно много решений, если выполнено условие a = 4.
Ответ: а=4.
Общий вид реш.
x = (-1)^k * arcsin(2/3) + pik, k ∈ Z
1)-3х²-4
2)-3(х+7)²
3)-3(х-2)²
4) -3х²+5
Это первое задание, сейчас остальные
1.S(треугольника) = b*h/2
S= 4*2/2= 4 см2
2.Без высоты не найти..
3.S=c*b
S=5*4 = 20см2
4.S=a*a
S= 9см2
5. S = a*c /2
S= 3*5=15см2