Chuyên đề 5: Hệ phương trình có đáp án

$\left\{\begin{array}{l}4x-y=7\\ x+3y=5\end{array}\right.\iff \left\{\begin{array}{l}12\text{x}-3y=21\\ x+3y=5\end{array}\right.\iff \left\{\begin{array}{l}13\text{x}=26\\ y=4\text{x}-7\end{array}\right.\iff \left\{\begin{array}{l}x=2\\ y=4.\text{2}-7\end{array}\right.\iff \left\{\begin{array}{l}x=2\\ y=1\end{array}\right.$

Vậy hệ phương trình có nghiệm duy nhất là: (x; y) = (2; 1)

$\left\{\begin{array}{l}2x-y=4\\ x+y=5\end{array}\right.\iff \left\{\begin{array}{l}3x=9\\ y=5-x\end{array}\right.\iff \left\{\begin{array}{l}x=3\\ y=2\end{array}\right.$

$\left\{\begin{array}{l}7x-3y=5\\ x+3y=3\end{array}\right.\iff \left\{\begin{array}{l}8x=8\\ x+3y=3\end{array}\right.\iff \left\{\begin{array}{l}x=1\\ x+3y=3\end{array}\right.\left\{\begin{array}{l}8x=8\\ y=\frac{2}{3}\end{array}\right.$

Chọn B

$\left\{\begin{array}{l}x-3y=-3\\ 3x+2y=13\end{array}\right.\iff \left\{\begin{array}{l}-3x+9y=9\\ 3x+2y=13\end{array}\right.\iff \left\{\begin{array}{l}11y=22\\ x-3y=-3\end{array}\right.\iff \left\{\begin{array}{l}y=2\\ x-3.2=-3\end{array}\right.\iff \left\{\begin{array}{l}x=3\\ y=2\end{array}\right.$

Chọn D

$\left\{\begin{array}{l}2x+3y=5\\ 3x-2y=-12\end{array}\right.\iff \left\{\begin{array}{l}6x+9y=15\\ 6x-4y=-24\end{array}\right.\iff \left\{\begin{array}{l}13y=39\\ x=\frac{5-3y}{2}\end{array}\right.\iff \left\{\begin{array}{l}y=3\\ x=-2\end{array}\right.$

Ta có $\left\{\begin{array}{l}3x-y=3\\ 2x+y=7\end{array}\right.\iff \left\{\begin{array}{l}5x=10\\ 2x+y=7\end{array}\right.\iff \left\{\begin{array}{l}x=2\\ 4+y=7\end{array}\right.\iff \left\{\begin{array}{l}x=2\\ y=3\end{array}\right.\Rightarrow \left(x;y\right)=\left(2;3\right)$

$\left\{\begin{array}{l}3x-y=5\\ 2y-x=0\end{array}\right.\iff \left\{\begin{array}{l}6y-y=5\\ x=2y\end{array}\right.\iff \left\{\begin{array}{l}y=1\\ x=2y\end{array}\right.\iff \left\{\begin{array}{l}x=2\\ y=1\end{array}\right.$

$\left\{\begin{array}{l}3x-4y=17\\ 5x+2y=11\end{array}\right.\iff \left\{\begin{array}{c}3x-4y=17\\ 10x+4y=22\end{array}\right.\iff \left\{\begin{array}{c}13x=39\\ 5x+2y=11\end{array}\right.\iff \left\{\begin{array}{c}x=3\\ 5.3+2y=11\end{array}\iff \left\{\begin{array}{c}x=3\\ y=-2\end{array}\right.\right.$

$\left\{\begin{array}{c}x+2y=5\\ x-5y=-9\end{array}\right.\iff \left\{\begin{array}{c}7y=14\\ x=5-2y\end{array}\right.\iff \left\{\begin{array}{c}y=2\\ x=5-2.2\end{array}\right.\iff \left\{\begin{array}{c}y=2\\ x=1\end{array}\right.$

$\left\{\begin{array}{l}x+y=2\\ 2x-y=1\end{array}\right.\iff \left\{\begin{array}{l}3x=3\\ y=2-x\end{array}\right.\iff \left\{\begin{array}{l}x=1\\ y=2-1\end{array}\right.\iff \left\{\begin{array}{l}x=1\\ y=1\end{array}\right.$

$\left\{\begin{array}{l}2x-y=5\\ x+y=1\end{array}\right.\iff \left\{\begin{array}{l}3x=6\\ y=1-x\end{array}\right.\iff \left\{\begin{array}{l}x=2\\ y=-1\end{array}\right.$

Vậy (x; y) = (2; -1)

$\left\{\begin{array}{l}x+y=5\\ 2x-y=1\end{array}\right.\iff \left\{\begin{array}{l}3x=6\\ y=5-x\end{array}\right.\iff \left\{\begin{array}{l}x=2\\ y=3\end{array}\right.$