a: \(\left\{{}\begin{matrix}3x-2y=11\\4x-5y=3\end{matrix}\right.\)

=>\(\left\{{}\begin{matrix}3x=11+2y\\4x-5y=3\end{matrix}\right.\)

=>\(\left\{{}\begin{matrix}x=\dfrac{2}{3}y+\dfrac{11}{3}\\4\left(\dfrac{2}{3}y+\dfrac{11}{3}\right)-5y=3\end{matrix}\right.\)

=>\(\left\{{}\begin{matrix}x=\dfrac{2}{3}y+\dfrac{11}{3}\\\dfrac{8}{3}y+\dfrac{44}{3}-5y=3\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{2}{3}y+\dfrac{11}{3}\\-\dfrac{7}{3}y=3-\dfrac{44}{3}=-\dfrac{35}{3}\end{matrix}\right.\)

=>\(\left\{{}\begin{matrix}y=5\\x=\dfrac{2}{3}\cdot5+\dfrac{11}{3}=\dfrac{10}{3}+\dfrac{11}{3}=\dfrac{21}{3}=7\end{matrix}\right.\)

b: \(\left\{{}\begin{matrix}\dfrac{x}{2}-\dfrac{y}{3}=1\\5x-8y=3\end{matrix}\right.\)

=>\(\left\{{}\begin{matrix}\dfrac{x}{2}=\dfrac{y}{3}+1\\5x-8y=3\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{2}{3}y+2\\5\left(\dfrac{2}{3}y+2\right)-8y=3\end{matrix}\right.\)

=>\(\left\{{}\begin{matrix}x=\dfrac{2}{3}y+2\\\dfrac{10}{3}y+10-8y=3\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}-\dfrac{14}{3}y=3-10=-7\\x=\dfrac{2}{3}y+2\end{matrix}\right.\)

=>\(\left\{{}\begin{matrix}y=7:\dfrac{14}{3}=7\cdot\dfrac{3}{14}=\dfrac{3}{2}\\x=\dfrac{2}{3}\cdot\dfrac{3}{2}+2=3\end{matrix}\right.\)

c: \(\left\{{}\begin{matrix}3x+5y=1\\2x-y=-8\end{matrix}\right.\)

=>\(\left\{{}\begin{matrix}y=2x+8\\3x+5\left(2x+8\right)=1\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}y=2x+8\\3x+10x+40=1\end{matrix}\right.\)

=>\(\left\{{}\begin{matrix}y=2x+8\\13x=-39\end{matrix}\right.\)

=>\(\left\{{}\begin{matrix}x=-3\\y=2\cdot\left(-3\right)+8=8-6=2\end{matrix}\right.\)

d: \(\left\{{}\begin{matrix}\dfrac{x}{y}=\dfrac{2}{3}\\x+y-10=0\end{matrix}\right.\)

=>\(\left\{{}\begin{matrix}x=\dfrac{2}{3}y\\x+y=10\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}\dfrac{2}{3}y+y=10\\x=\dfrac{2}{3}y\end{matrix}\right.\)

=>\(\left\{{}\begin{matrix}\dfrac{5}{3}y=10\\x=\dfrac{2}{3}y\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}y=6\\x=\dfrac{2}{3}\cdot6=4\end{matrix}\right.\)

a) \(\left\{{}\begin{matrix}x+2y-3z=2\\2x+7y+z=5\\-3x+3y-2z=-7\end{matrix}\right.\)\(\Leftrightarrow\left\{{}\begin{matrix}x+2y-3z=2\\3y+7z=1\\-32z=-4\end{matrix}\right.\)

Đáp số : \(\left(x,y,z\right)=\left(\dfrac{55}{24},\dfrac{1}{24},\dfrac{1}{8}\right)\)

b) \(\left\{{}\begin{matrix}-x-3y+4z=3\\3x+4y-2z=5\\2x+y+2z=4\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}-x-3y+4z=3\\-5y+10z=14\\-5y+10z=10\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}-x-3y+4z=3\\-5y+10z=14\\0y+0z=-4\end{matrix}\right.\)

Phương trình cuối vô nghiệm, suy ra hệ phương trình đã cho vô nghiệm

a. \(\left\{{}\begin{matrix}3x-5y=6\\4x+7y=-8\end{matrix}\right.\)

\(x=\dfrac{2}{41}\) ; \(y=\dfrac{-48}{41}\)

b.

\(x=\dfrac{2}{19};y=\dfrac{33}{19}\)

c.

\(x=\dfrac{22}{101};y=\dfrac{131}{101};z=\dfrac{-39}{101}\)

d.

\(x=-4;y=\dfrac{11}{7};z=\dfrac{12}{7}\)

a)x=0,05 ; y=-1,17

b.x=0,11 ; y=1,74

c.x=0,22 ;y=1,29 z=-0.39

d.x=-4 y=1,57 z=1,71

a,\(\left\{{}\begin{matrix}3x-5y=6\\4x+7y=-8\end{matrix}\right.\)

x=\(\dfrac{2}{41}=0,05\) ; y=\(\dfrac{-48}{41}=-1,17\)

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

x=\(\dfrac{2}{19}=0,11\) ; y=\(\dfrac{33}{19}=1,74\)

c,\(\left\{{}\begin{matrix}2x-3y+4z=-5\\-4x+5y-z=6\\3x+4y-3z=2\end{matrix}\right.\)

x=\(\dfrac{22}{101}=0,22\) ;y=\(\dfrac{131}{101}=1,29\) ; z=\(\dfrac{-39}{101}=-0,39\)

d,\(\left\{{}\begin{matrix}-x+2y-3z=2\\2x+y+2z=-3\\-2x-3y+z=5\end{matrix}\right.\)

x=\(-4\) ; y=\(\dfrac{11}{7}=1,57\) ; z=\(\dfrac{12}{7}=1,71\)

b) Đặt \(\left\{{}\begin{matrix}x+y+z=7\left(1\right)\\3x-2y+2z=5\left(2\right)\\4x-y+3z=10\left(3\right)\end{matrix}\right.\)
Cộng \(\left(1\right)+\left(2\right)\) ta có: \(4x-y+3z=12\). (4)
Từ (3) và (4): \(\left\{{}\begin{matrix}4x-y+3z=12\\4x-y+3z=10\end{matrix}\right.\) (vô nghiệm).
Vậy hệ phương trình vô nghiệm.

a)\(pt\left(2\right)\Leftrightarrow\left(5t-z\right)^2=0\Rightarrow z=5t\)

\(pt\left(3\right)\Leftrightarrow\left(x-2y\right)^2+\left(y-2z\right)^2=0\Rightarrow....\)

b)vĩ đại vậy chắc xài BĐT thôi, loanh quanh C-S và AM-GM 3 số