Question

Розв'яжіть систему рівнянь
1) {7x+2y=-3-14x + 3y= 20.
2) {7(x + 3) = 3y + 14(2 - x) = 5(y + 1) + 1​.​

Answer 1

Ответ:

Применим метод сложения решения систем линейных уравнений .

$1)\ \ \left\{\begin{array}{l}7x+2y=-3\ |\cdot 2\\-14x+3y=20\end{array}\right\ \oplus \ \left\{\begin{array}{l}7x+2y=-3\\4y+3y=-6+20\end{array}\right\ \ \left\{\begin{array}{l}7x=-2y-3\\7y=14\end{array}\right\\\\\\\left\{\begin{array}{l}7x=-2\cdot 2-3\\y=2\end{array}\right\ \ \left\{\begin{array}{l}7x=-7\\y=2\end{array}\right\ \ \left\{\begin{array}{l}\ x=-1\\y=2\end{array}\right\\\\\\Otvet:\ \ \Big(-1\ ;\ 2\ \Big)\ .$  

$2)\ \ \left\{\begin{array}{l}7(x+3)=3y+14\\(2-x)=5(y+1)+1\end{array}\right\ \ \left\{\begin{array}{l}7x+21=3y+14\\2-x=5y+5+1\end{array}\right\ \ \left\{\begin{array}{l}7x-3y=-7\\-x-5y=4\ |\cdot 7\end{array}\right\oplus$

$\left\{\begin{array}{l}-38y=21\\-x-5y=4\end{array}\right\ \ \left\{\begin{array}{l}y=-\dfrac{21}{38}\\x=-5y-4\end{array}\right\ \ \left\{\begin{array}{l}y=-\dfrac{21}{38}\\\, x=\dfrac{105}{38}-4\end{array}\right\ \ \left\{\begin{array}{l}y=-\dfrac{21}{38}\\\ x=-\dfrac{47}{38}\end{array}\right\\\\\\Otvet:\ \Big(-\dfrac{47}{38}\ ;-\dfrac{21}{38}\ \Big)\ .$