Question

[NeyuQ Nguyễn]

Giải HPT theo phương pháp cộng đại số

c) \(\left\{{}\begin{matrix}-2x+3y=1\\\dfrac{1}{3}x-\dfrac{1}{2}y=\dfrac{-1}{6}\end{matrix}\right.\)

Answer 1

[Nguyễn Lê Phước Thịnh]

\(\left\{{}\begin{matrix}-2x+3y=1\\\dfrac{1}{3}x-\dfrac{1}{2}y=-\dfrac{1}{6}\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}-\dfrac{2}{3}x+y=\dfrac{1}{3}\\\dfrac{2}{3}x-y=-\dfrac{1}{3}\end{matrix}\right.\)

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

=>\(\left\{{}\begin{matrix}0x=0\\y=\dfrac{2}{3}x+\dfrac{1}{3}\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x\in R\\y=\dfrac{2x+1}{3}\end{matrix}\right.\)

Answer 2

[Phạm Trần Hoàng Anh]

\(\left\{{}\begin{matrix}-2x+3y=1\\\dfrac{1}{3}x-\dfrac{1}{2}y=-\dfrac{1}{6}\end{matrix}\right.=>\left\{{}\begin{matrix}-2x+3y=1\\2x-3y=-1\end{matrix}\right.=>\left\{{}\begin{matrix}0x=0\\-2x+3y=1\end{matrix}\right.\)

Vậy có vô số nghiệm