Câu 1 : \(a,\hept{\begin{cases}4x+7y=16\left(1\right)\\4x-3y=-24\left(2\right)\end{cases}}\)

Lấy ( 1 ) trừ ( 2 ) ta được :

10y = 40

=> y = 4

Thay y = 4 vào ( 1 ) ta được :

4x + 7 x 4 = 16 

=> 4x + 28 = 16

=> 4x = 16 - 28 

=> 4x = - 12

=> x = - 3

Vậy x = - 3 ; y = 4 

\(b,\hept{\begin{cases}3x+5y=1\\2x+y=-4\end{cases}}\)

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

\(\Leftrightarrow\hept{\begin{cases}3x-20-10x=1\\y=-4-2x\end{cases}}\)

\(\Leftrightarrow\hept{\begin{cases}-7x-20=1\\y=-4-2x\end{cases}}\)

\(\Leftrightarrow\hept{\begin{cases}-7x=21\\y=-4-2x\end{cases}}\)

\(\Leftrightarrow\hept{\begin{cases}x=-3\\y=-4-2.\left(-3\right)\end{cases}}\)

\(\Leftrightarrow\hept{\begin{cases}x=-3\\y=2\end{cases}}\)

Câu 1 : \(a,\hept{\begin{cases}4x+7y=16\left(1\right)\\4x-3y=-24\left(2\right)\end{cases}}\)

Lấy ( 1 ) trừ  ( 2 ) ta được :

10y = 40 

=> y = 4

Thay y = 4 vào ( 1 ) ta được :

4x + 7 . 4 = 16

=> 4x + 28 = 16

=> 4x = 16 - 28

=> 4x = -12

=> x = - 3

Vậy x = - 3 ; y = 4

\(b,\hept{\begin{cases}3x+5y=1\\2x+y=-4\end{cases}}\)

\(\Leftrightarrow\hept{\begin{cases}6x+10y=2\left(1\right)\\6x+3y=-12\left(2\right)\end{cases}}\)

Lấy ( 1 ) trừ ( 2 ) ta được :

7y = 14

=> y = 2

Thay y = 2 vào ( 1 ) 

Ta được : 6x + 10 . 2 = 2

=> 6x + 20 = 2

=> 6x = 2 - 20

=> 6x = - 18

=> x= - 3

Vậy x = - 3 ; y = 2

Bài 1: 

3x+2y=7

\(\Leftrightarrow3x=7-2y\)

\(\Leftrightarrow x=\dfrac{7-2y}{3}\)

Vậy: \(\left\{{}\begin{matrix}y\in R\\x=\dfrac{7-2y}{3}\end{matrix}\right.\)

giúp mình nhé

\(1,3x+2y=7\\ \Leftrightarrow2y=7-3x\left(1\right)\)

Vì \(2y⋮2\)

\(\Leftrightarrow3x-7⋮2\\ \Leftrightarrow3x-9⋮2\\ \Leftrightarrow3\left(x-3\right)⋮2\\ \Leftrightarrow x-3⋮2\\ \Leftrightarrow x.lẻ\)

Đặt \(x=2k+1\left(k\in Z\right)\)

Thay vào (1), ta được :

\(\left(1\right)\Leftrightarrow2y=3\left(2k+1\right)-7\\ \Leftrightarrow2y=6k+3-7\\ \Leftrightarrow2y=6k-4\\ \Leftrightarrow y=3k-2\)

Vậy \(x=2k+1;y=3k-2\left(k\in Z\right)\)

\(2,C_1:\left\{{}\begin{matrix}-2x+y=1\\4x+5y=3\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}-4x+2y=2\\4x+5y=3\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}4x+5y=2\\7y=5\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=-\dfrac{1}{7}\\y=\dfrac{5}{7}\end{matrix}\right.\\ C_2:\left\{{}\begin{matrix}-2x+y=1\\4x+5y=3\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}y=1+2x\\4x+5y=3\end{matrix}\right.\Leftrightarrow4x+5+10x=3\\ \Leftrightarrow x=-\dfrac{1}{7}\Leftrightarrow y=1-\dfrac{2}{7}=\dfrac{5}{7}\)

a) \(\sqrt{4x^2-4x+9}=3\)

Vì \(4x^2-4x+9=\left(2x-1\right)^2+8>0\)( Với mọi x )

Nên \(\sqrt{4x^2-4x+9}=3\)

⇔\(4x^2-4x+9=9\)

⇔\(4x^2-4x=0\)

⇔\(4x\left(x-1\right)=0\)

⇔\(\left[{}\begin{matrix}4x=0\\x-1=0\end{matrix}\right.\)

⇔\(\left[{}\begin{matrix}x=0\\x=1\end{matrix}\right.\)

Vậy \(\left[{}\begin{matrix}x=0\\x=1\end{matrix}\right.\)là nghiệm

a: Ta có: \(\left\{{}\begin{matrix}2x-10y=-7\\10x+11y=31\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}10x-50y=-35\\10x+10y=31\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}-60y=-66\\2x-10y=-7\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}y=\dfrac{11}{10}\\2x=-7+10y=-7+11=8\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=4\\y=\dfrac{11}{10}\end{matrix}\right.\)