Bài 2. Phương trình bậc nhất hai ẩn và hệ hai phương trình bậc nhất hai ẩn

a:

C1: \(\left\{{}\begin{matrix}-3x+y=4\\7x+5y=-2\end{matrix}\right.\)

=>\(\left\{{}\begin{matrix}-15x+5y=20\\7x+5y=-2\end{matrix}\right.\)

=>\(\left\{{}\begin{matrix}-15x+5y-7x-5y=20-\left(-2\right)\\-3x+y=4\end{matrix}\right.\)

=>\(\left\{{}\begin{matrix}-22x=22\\y=3x+4\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=-1\\y=3\cdot\left(-1\right)+4=4-3=1\end{matrix}\right.\)

C2: \(\left\{{}\begin{matrix}-3x+y=4\\7x+5y=-2\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}y=3x+4\\7x+5\left(3x+4\right)=-2\end{matrix}\right.\)

=>\(\left\{{}\begin{matrix}y=3x+4\\22x+20=-2\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}22x=-22\\y=3x+4\end{matrix}\right.\)

=>\(\left\{{}\begin{matrix}x=-1\\y=3\cdot\left(-1\right)+4=4-3=1\end{matrix}\right.\)

b: 

C1: \(\left\{{}\begin{matrix}2x-5y=-9\\3x+4y=-2\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}2x=5y-9\\3x+4y=-2\end{matrix}\right.\)

=>\(\left\{{}\begin{matrix}x=\dfrac{5}{2}y-\dfrac{9}{2}\\3\left(\dfrac{5}{2}y-\dfrac{9}{2}\right)+4y=-2\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{5}{2}y-\dfrac{9}{2}\\\dfrac{15}{2}y-\dfrac{27}{2}+4y=-2\end{matrix}\right.\)

=>\(\left\{{}\begin{matrix}\dfrac{23}{2}y=-2+\dfrac{27}{2}=\dfrac{23}{2}\\x=\dfrac{5}{2}y-\dfrac{9}{2}\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}y=1\\x=\dfrac{5}{2}-\dfrac{9}{2}=-\dfrac{4}{2}=-2\end{matrix}\right.\)

C2: \(\left\{{}\begin{matrix}2x-5y=-9\\3x+4y=-2\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}8x-20y=-36\\15x+20y=-10\end{matrix}\right.\)

=>\(\left\{{}\begin{matrix}8x-20y+15x+20y=-36+\left(-10\right)\\2x-5y=-9\end{matrix}\right.\)

=>\(\left\{{}\begin{matrix}23x=-46\\5y=2x+9\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=-2\\5y=2\cdot\left(-2\right)+9=5\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=-2\\y=1\end{matrix}\right.\)

\(\left\{{}\begin{matrix}7x+4y=1\\3x-2y=9\end{matrix}\right.\)

=>\(\left\{{}\begin{matrix}7x+4y=1\\6x-4y=18\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}7x+4y+6x-4y=1+18\\3x-2y=9\end{matrix}\right.\)

=>\(\left\{{}\begin{matrix}13x=19\\2y=3x-9\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{19}{13}\\y=\dfrac{3}{2}x-\dfrac{9}{2}=\dfrac{3}{2}\cdot\dfrac{19}{13}-\dfrac{9}{2}=\dfrac{57}{26}-\dfrac{9}{2}=-\dfrac{30}{13}\end{matrix}\right.\)