<span>{4(y-3x)-5(y-4x)=-10
{6(x-2y)+5y=-20
{4y-12x-5y+20x=-10
{6x-12y+5y=-20
{-y+8x=-10 { y=8x+10 </span>{ y=8x+10 { y=8x+10<span>
{6x-7y=-20 {6x-7(8x+10)=-20 {6x-56x-70=-20 {-50x=50
</span>{y=8x+10 {y=-8+10 {y=2
{x=-1 {x=-1 {x=-1
ответ (-1;2)
- функция, которая задаёт прямую.
- функция, которая задаёт параболу.
Достаточно того, что бы эти точки лежали и на прямой и на параболе. Поэтому целесообразно составить две системы, которые получаются путём подстановки абсцисс и ординат точек пересечения в исходные функции. Точки пересечения A(-4;4) и B(-6; 10).
![\begin{cases}4 = -4k + l\\ 10 = -6k + l\end{cases}\\\\ \begin{cases} 4 + 4k = l\\ 10 = -6k + l\end{cases}\\\\ \begin{cases} 4 + 4k = l\\ 10 = -6k + 4 + 4k\end{cases}\\\\ \begin{cases} 4 + 4k = l\\ 6 = -2k \end{cases}\\\\ \begin{cases} 4 + 4(-3) = l\\ k = -3\end{cases}\\\\ \begin{cases} l = -8\\ k = -3 \end{cases}\\\\ y = -3x - 8](https://tex.z-dn.net/?f=%5Cbegin%7Bcases%7D4+%3D+-4k+%2B+l%5C%5C+10+%3D+-6k+%2B+l%5Cend%7Bcases%7D%5C%5C%5C%5C+%5Cbegin%7Bcases%7D+4+%2B+4k+%3D+l%5C%5C+10+%3D+-6k+%2B+l%5Cend%7Bcases%7D%5C%5C%5C%5C+%5Cbegin%7Bcases%7D+4+%2B+4k+%3D+l%5C%5C+10+%3D+-6k+%2B+4+%2B+4k%5Cend%7Bcases%7D%5C%5C%5C%5C+%5Cbegin%7Bcases%7D+4+%2B+4k+%3D+l%5C%5C+6+%3D+-2k+%5Cend%7Bcases%7D%5C%5C%5C%5C+%5Cbegin%7Bcases%7D+4+%2B+4%28-3%29+%3D+l%5C%5C+k+%3D+-3%5Cend%7Bcases%7D%5C%5C%5C%5C+%5Cbegin%7Bcases%7D+l+%3D+-8%5C%5C+k+%3D+-3+%5Cend%7Bcases%7D%5C%5C%5C%5C+y+%3D+-3x+-+8)
![\begin{cases} 4 = 16 - 4b + c\\ 10 = 36 - 6b + c \end{cases}\\\\ \begin{cases} -12 + 4b = c\\ 10 = 36 - 6b - 12 + 4b \end{cases}\\\\ \begin{cases} -12 + 4b = c\\ -14 =-2b \end{cases}\\\\ \begin{cases} -12 + 4*7 = c\\ b = 7 \end{cases}\\\\ \begin{cases} c = 16\\ b = 7 \end{cases}\\\\ y = x^2 + 7x + 16](https://tex.z-dn.net/?f=%5Cbegin%7Bcases%7D+4+%3D+16+-+4b+%2B+c%5C%5C+10+%3D+36+-+6b+%2B+c+%5Cend%7Bcases%7D%5C%5C%5C%5C+%5Cbegin%7Bcases%7D+-12+%2B+4b+%3D+c%5C%5C+10+%3D+36+-+6b+-+12+%2B+4b+%5Cend%7Bcases%7D%5C%5C%5C%5C+%5Cbegin%7Bcases%7D+-12+%2B+4b+%3D+c%5C%5C+-14+%3D-2b+%5Cend%7Bcases%7D%5C%5C%5C%5C+%5Cbegin%7Bcases%7D+-12+%2B+4%2A7+%3D+c%5C%5C+b+%3D+7+%5Cend%7Bcases%7D%5C%5C%5C%5C+%5Cbegin%7Bcases%7D+c+%3D+16%5C%5C+b+%3D+7+%5Cend%7Bcases%7D%5C%5C%5C%5C+y+%3D+x%5E2+%2B+7x+%2B+16)
![\fbox{k = -3, l = -8, b = 7, c = 16}](https://tex.z-dn.net/?f=+%5Cfbox%7Bk+%3D+-3%2C+l+%3D+-8%2C+b+%3D+7%2C+c+%3D+16%7D)
по формуле <span>cos^2(2x)-sin^2(2x)=0</span>
Решение задания приложено