Question

Giải hệ pt :

a) \(\left\{{}\begin{matrix}12x+16y+1=0\\3x+4y+2=0\end{matrix}\right.\)

b) \(\left\{{}\begin{matrix}\dfrac{5x-1}{5y-2}=\dfrac{1}{2}\\5 \left(x+3\right)-7\left(y+1\right)=-1\end{matrix}\right.\)

Answer 1

a)\(\Leftrightarrow\left\{{}\begin{matrix}12x+16y=-1\\3x+4y=-2\end{matrix}\right.\)(vô nghiệm)

Vậy hpt vô nghiệm.

b)\(\left\{{}\begin{matrix}\dfrac{5x-1}{5y-1}=\dfrac{1}{2}\\5x-7y=-9\end{matrix}\right.\)\(\Rightarrow\left\{{}\begin{matrix}10x-2=10y-1\\5x-7y=-9\end{matrix}\right.\)\(\Leftrightarrow\left\{{}\begin{matrix}10x-10y=1\\5x-7y=-9\end{matrix}\right.\)\(\Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{97}{20}\\y=\dfrac{19}{4}\end{matrix}\right.\)

Vậy hpt có tập nghiệm là \(\left(\dfrac{97}{20};\dfrac{19}{4}\right)\).

Answer 2