Question

Решите методом крамера {3x+7y=-1 5x+9y=1

Answer 1

$\begin{cases}3x+7y=-1\\5x+9y=1\end{cases}\\\\A=\left(\begin{array}{cc}3&7\\5&9\end{array}\right)\\B=\left(\begin{array}{c}-1\\1\end{array}\right)\\\\\Delta=\left|\begin{array}{cc}3&7\\5&9\end{array}\right|=3\cdot9-7\cdot5=27-35=-8\\\\\\\Delta_1=\left|\begin{array}{cc}-1&7\\1&9\end{array}\right|=-1\cdot9-7\cdot1=-9-7=-16\\\\x_1=\frac{\Delta_1}{\Delta}=\frac{-16}{-8}=2\\\\\\\Delta_2=\left|\begin{array}{cc}3&-1\\5&1\end{array}\right|=3\cdot1-(-1)\cdot5=3+5=8\\\\x_2=\frac{\Delta_2}{\Delta}=\frac8{-8}=-1$