Đáp án + giải thích các bước giải:
a) $\left\{\begin{matrix} 7x-2y=1\\3x+y=6 \end{matrix}\right.\\\to\left\{\begin{matrix} 7x-2y=1\\6x+2y=12 \end{matrix}\right.\\\to \left\{\begin{matrix} 7x-2y+6x+2y=1+12\\3x+y=6 \end{matrix}\right.\\\to\left\{\begin{matrix} 13x=13\\3x+y=6 \end{matrix}\right.\\\to \left\{\begin{matrix} x=1\\3+y=6 \end{matrix}\right.\\\to \left\{\begin{matrix} x=1\\y=3\end{matrix}\right.$
Vậy `(x;y)=(1;3)`
b) $\left\{\begin{matrix} \sqrt{5}x-y=\sqrt{5}(\sqrt{3}-1)\\2\sqrt{3}x+3\sqrt{5}y=21 \end{matrix}\right.\\\to \left\{\begin{matrix} 15x-3\sqrt{5}y=15(\sqrt{3}-1)\\2\sqrt{3}x+3\sqrt{5}y=21 \end{matrix}\right.\\\to \left\{\begin{matrix} 15x-3\sqrt{5}y+2\sqrt{3}x+3\sqrt{5}y=15(\sqrt{3}-1)+21\\2\sqrt{3}x+3\sqrt{5}y=21 \end{matrix}\right.\\\to \left\{\begin{matrix} (15+2\sqrt{3})x=6+15\sqrt{3}\\2\sqrt{3}x+3\sqrt{5}y=21 \end{matrix}\right.\\\to \left\{\begin{matrix} x=\sqrt{3}\\6+3\sqrt{5}y=21 \end{matrix}\right. \\\to\left\{\begin{matrix} x=\sqrt{3}\\y=\sqrt{5} \end{matrix}\right. $
Vậy `(x;y)=(\sqrt{3};\sqrt{5})`
c) $\left\{\begin{matrix} -0,5x+1,2y=2,7\\x-4,5y=-7,5 \end{matrix}\right.\\\to \left\{\begin{matrix} -x+2,4y=5,4\\x-4,5y=-7,5 \end{matrix}\right. \\\to \left\{\begin{matrix} -x+2,4y+x-4,5y=5,4-7,5\\x-4,5y=-7,5 \end{matrix}\right.\\\to \left\{\begin{matrix} -2,1y=-2,1\\x-4,5y=-7,5 \end{matrix}\right. \\\to \left\{\begin{matrix} y=1\\x-4,5=-7,5 \end{matrix}\right.\\\to \left\{\begin{matrix} x=-3\\y=1 \end{matrix}\right.$
Vậy `(x;y)=(-3;1)`
d) $ \left\{\begin{matrix} \dfrac{x}{3}-\dfrac{y}{4}=2\\\dfrac{2x}{5}+y=18 \end{matrix}\right.\\\to \left\{\begin{matrix} \dfrac{4x}{3}-y=8\\\dfrac{2x}{5}+y=18 \end{matrix}\right.\\\to \left\{\begin{matrix} \dfrac{4x}{3}-y+\dfrac{2x}{5}+y=8+18\\\dfrac{2x}{5}+y=18 \end{matrix}\right.\\\to \left\{\begin{matrix} \dfrac{26x}{15}=26\\\dfrac{2x}{5}+y=18 \end{matrix}\right. \\\to \left\{\begin{matrix} x=15\\6+y=18 \end{matrix}\right.\\\to \left\{\begin{matrix} x=15\\y=12 \end{matrix}\right.$
Vậy `(x;y)=(15;12)`
