a: \(\begin{cases}3x-y=5\\ 4x+2y=10\end{cases}\)

=>\(\begin{cases}3x-y=5\\ 2x+y=5\end{cases}\Rightarrow\begin{cases}3x-y+2x+y=5+5\\ 2x+y=5\end{cases}\)

=>\(\begin{cases}5x=10\\ 2x+y=5\end{cases}\Rightarrow\begin{cases}x=2\\ y=5-2\cdot2=5-4=1\end{cases}\)

b: \(\begin{cases}5x+2y=9\\ x+5y=11\end{cases}\Rightarrow\begin{cases}5x+2y=9\\ 5x+25y=55\end{cases}\)

=>\(\begin{cases}5x+25y-5x-2y=55-9\\ x+5y=11\end{cases}\Rightarrow\begin{cases}23y=46\\ x=11-5y\end{cases}\)

=>\(\begin{cases}y=2\\ x=11-5\cdot2=11-10=1\end{cases}\)

c: \(\begin{cases}3x+y=10\\ 4x-3y=9\end{cases}\Rightarrow\begin{cases}9x+3y=30\\ 4x-3y=9\end{cases}\)

=>\(\begin{cases}9x+3y+4x-3y=30+9\\ 3x+y=10\end{cases}\Rightarrow\begin{cases}13x=39\\ y=10-3x\end{cases}\)

=>\(\begin{cases}x=3\\ y=10-3\cdot3=10-9=1\end{cases}\)

d: \(\begin{cases}4x+3y=22\\ 5x+3y=26\end{cases}\Rightarrow\begin{cases}5x+3y-4x-3y=26-22\\ 4x+3y=22\end{cases}\)

=>\(\begin{cases}x=4\\ 3y=22-4x=22-4\cdot4=22-16=6\end{cases}\Rightarrow\begin{cases}x=4\\ y=2\end{cases}\)

\(a,\left\{{}\begin{matrix}3x-y=5\\4x+2y=10\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}3x-y=5\\2x+y=5\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=2\\y=1\end{matrix}\right.\\ b,\left\{{}\begin{matrix}5x+2y=9\\x+5y=11\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}5x+2y=9\\5x+25y=55\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}5x+2y=9\\23y=46\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=1\\y=2\end{matrix}\right.\)

\(c,\left\{{}\begin{matrix}3x+y=10\\4x-3y=9\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}9x+3y=30\\4x-3y=9\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}13x=39\\4x-3y=9\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=3\\y=1\end{matrix}\right.\\ d,\left\{{}\begin{matrix}4x+3y=22\\5x+3y=26\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=4\\5x+3y=26\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=4\\y=2\end{matrix}\right.\)

\(e,\left\{{}\begin{matrix}4x-3y=5\\5x+3y=13\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}9x=18\\5x+3y=13\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=2\\y=1\end{matrix}\right.\)

a. \(\left\{{}\begin{matrix}3x-y=5\\4x+2y=10\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}6x-2y=10\\4x+2y=10\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}10x=20\\6x-2y=10\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=2\\y=1\end{matrix}\right.\)

b. \(\left\{{}\begin{matrix}5x+2y=9\\x+5y=11\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}5x+2y=9\\5x+25y=55\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}23y=46\\5x+2y=9\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}y=2\\x=1\end{matrix}\right.\)

c. \(\left\{{}\begin{matrix}3x+y=10\\4x-3y=9\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}9x+3y=30\\4x-3y=9\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}13x=39\\4x-3y=9\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=3\\y=1\end{matrix}\right.\)

d. \(\left\{{}\begin{matrix}4x+3y=22\\5x+3y=26\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=4\\4x+3y=22\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=4\\y=2\end{matrix}\right.\)

e. \(\left\{{}\begin{matrix}4x-3y=5\\5x+3y=13\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}9x=18\\4x-3y=5\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=2\\y=1\end{matrix}\right.\)

\(\hept{\begin{cases}4x+y=-5\\3x-2y=-12\end{cases}\Leftrightarrow\hept{\begin{cases}8x+2y=-10\\3x-2y=-12\end{cases}}\Leftrightarrow\hept{\begin{cases}8x+2y=-10\\11x=-22\end{cases}}}\)

\(\Leftrightarrow\hept{\begin{cases}8x+2y=-10\\x=-2\end{cases}}\Leftrightarrow\hept{\begin{cases}8\left(-2\right)+2y=-10\\x=-2\end{cases}\Leftrightarrow\hept{\begin{cases}2y=6\\x=-2\end{cases}}\Leftrightarrow\hept{\begin{cases}y=3\\x=-2\end{cases}}}\).

\(\hept{\begin{cases}4x+y=-5\\3x-2y=-12\end{cases}\Leftrightarrow\hept{\begin{cases}y=-5-4x\left(1\right)\\3x-2y=-12\left(2\right)\end{cases}}}\)

Thay y vào pt (2) ta đc : \(3x-2\left(-5-4x\right)=-12\)

\(\Leftrightarrow3x+10+8x=-12\Leftrightarrow11x+22=0\)

\(\Leftrightarrow11x=-22\Leftrightarrow x=-2\)

Thay x vào pt (1) ta đc : \(y=-5-4.\left(-2\right)=-5+8=3\)

Vậy \(\left\{x;y\right\}=\left\{-2;3\right\}\)

Vậy hệ phương trình đã cho có nghiệm (x; y) = (56; -9).

\(a,\left\{{}\begin{matrix}2x-y=1\\3x+2y=5\end{matrix}\right.\\ =>\left\{{}\begin{matrix}4x-2y=2\\3x+2y=5\end{matrix}\right.\\ =>\left\{{}\begin{matrix}7x=7\\2x-y=1\end{matrix}\right.\\ =>\left\{{}\begin{matrix}x=1\\2.1-y=1\end{matrix}\right.\\ =>\left\{{}\begin{matrix}x=1\\y=1\end{matrix}\right.\)

Vậy \(\left(x;y\right)=\left(1;1\right)\)

\(b,\left\{{}\begin{matrix}4x+3y=-1\\3x-2y=2\end{matrix}\right.\\ =>\left\{{}\begin{matrix}4.2x+3.2y=-1.2\\3.3x-2.3y=2.3\end{matrix}\right.\\ =>\left\{{}\begin{matrix}8x+6y=-2\\9x-6y=6\end{matrix}\right.\\ =>\left\{{}\begin{matrix}17x=4\\3x-2y=2\end{matrix}\right.\\ =>\left\{{}\begin{matrix}x=\dfrac{4}{17}\\y=-\dfrac{11}{17}\end{matrix}\right.\)

Vậy \(\left(x;y\right)=\left(\dfrac{4}{17};-\dfrac{11}{17}\right)\)

a: Để hệ có vô số nghiệm thì \(\frac{4}{m}=\frac{-1}{1}=\frac{3}{-3}=-1\)

=>m=-4

b: Để hệ có vô số nghiệm thì \(\frac13=\frac26=\frac{m}{12}\)

=>\(\frac{m}{12}=\frac13=\frac{4}{12}\)

=>m=4

a: Để hệ có vô số nghiệm thì \(\frac{4}{m}=\frac{-1}{1}=\frac{3}{-3}=-1\)

=>m=-4

b: Để hệ có vô số nghiệm thì \(\frac13=\frac26=\frac{m}{12}\)

=>\(\frac{m}{12}=\frac13\)

=>m=4