a: \(\Leftrightarrow\left\{{}\begin{matrix}3x+5y+4x-5y=34-13=21\\4x-5y=-13\\5x-2y=5\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}x=3\\12-5y=-13\\15-2y=5\end{matrix}\right.\Leftrightarrow\left(x,y\right)=\left(3;5\right)\)

b: \(\left\{{}\begin{matrix}-3x+2y=22\\6x-5y+7x+5y=-49+10\\7x+5y=10\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}13x=-39\\-3x+2y=22\\7x+5y=10\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=-3\\2y+9=22\\5y-21=10\end{matrix}\right.\Leftrightarrow\left(x,y\right)\in\varnothing\)

Thay x = -3, y = 31/5 vào vế trái của phương trình (2), ta được:

VT = -3.(-3) + 2.31/5 = 9 + 62/5 = 107/5 ≠ 22 = VP

Vậy (x; y) = (-3; 31/5 ) không phải là nghiệm của phương trình (2).

Hệ phương trình đã cho vô nghiệm.

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

Cộng vế hai biểu thức ta đc \(7x=21\)=> x =3 

thay vào ta tìm đc y=5

_Kudo_

nhâ vế 1 vs 2

nhân vế 2 vs 3 là ra thôi bn

trừ 2 vế cho nhau nữa

\(\left\{{}\begin{matrix}3x+2y=4\\2x-3y=7\end{matrix}\right.< =>\left\{{}\begin{matrix}6x+4y=8\\6x-9y=21\end{matrix}\right.\)

\(< =>\left\{{}\begin{matrix}13y=-13\\3x+2y=4\end{matrix}\right.< =>\left\{{}\begin{matrix}y=-1\\3x=4+2=6\end{matrix}\right.\)

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