a)\(\left\{{}\begin{matrix}8x+2y=4\\8x+3y=5\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}y=1\\4x+1=2\end{matrix}\right.\Leftrightarrow}\left\{{}\begin{matrix}y=1\\x=\frac{1}{4}\end{matrix}\right.\)b)

\(\left\{{}\begin{matrix}12x-8y=44\\12x-15y=9\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}7y=35\\4x-5y=3\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}y=5\\4x-5.5=3\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}y=5\\x=7\end{matrix}\right.\)c)\(\left\{{}\begin{matrix}9x=-18\\4x+3y=13\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=-2\\4.\left(-2\right)+3y=13\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=-2\\y=7\end{matrix}\right.\)

các câu khác tương tự

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

<=> \(\left\{{}\begin{matrix}3x-2y=4\\7x=14\end{matrix}\right.< =>\left\{{}\begin{matrix}x=2\\y=1\end{matrix}\right.\)

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

=> Hệ có vô số nghiệm.

3)\(\left\{{}\begin{matrix}3x-4y=-2\\10x+4y=28\end{matrix}\right.\)

<=>\(\left\{{}\begin{matrix}3x-4y=-2\\13x=26\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=2\\y=2\end{matrix}\right.\)

4)\(\left\{{}\begin{matrix}6x+15y=9\\6x-4y=28\end{matrix}\right.\)

<=>\(\left\{{}\begin{matrix}6x+15y=9\\19y=19\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=4\\y=-1\end{matrix}\right.\)

e.

\(\left\{{}\begin{matrix}2x-3y+5=0\\3x+5y-21=0\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}10x-15y=-25\\9x+15y=63\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}19x=38\\3x+5y=21\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}x=2\\y=\dfrac{21-3x}{5}\end{matrix}\right.\)

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

f.

\(\left\{{}\begin{matrix}x-y\sqrt{2}=0\\2x\sqrt{2}+y=5\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}x-y\sqrt{2}=0\\4x+y\sqrt{2}=5\sqrt{2}\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}5x=5\sqrt{2}\\2x\sqrt{2}+y=5\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}x=\sqrt{2}\\y=5-2x\sqrt{2}\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}x=\sqrt{2}\\y=1\end{matrix}\right.\)

a.

\(\Leftrightarrow\left\{{}\begin{matrix}5x=-25\\3x-5y=-30\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}x=-5\\y=\dfrac{3x+30}{5}\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}x=-5\\y=3\end{matrix}\right.\)

b.

\(\Leftrightarrow\left\{{}\begin{matrix}8x-6y=-10\\9x+6y=-24\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}17x=-34\\9x+6y=-24\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}x=-2\\y=\dfrac{-24-9x}{6}\end{matrix}\right.\)

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

c.

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

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

\(\Leftrightarrow\left\{{}\begin{matrix}3x=2\\2x-y=-1\end{matrix}\right.\)

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

\(\Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{2}{3}\\y=\dfrac{7}{3}\end{matrix}\right.\)

d.

\(\left\{{}\begin{matrix}5x-4y=32\\6x+2y=18\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}5x-4y=32\\12x+4y=36\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}5x-4y=32\\17x=68\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}x=4\\y=\dfrac{3x-32}{4}\end{matrix}\right.\)

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

\(a) \begin{cases}x=y+4\\2x+3=0\end{cases}\Leftrightarrow\begin{cases}x = y + 4\\2x = -3\end{cases}\Leftrightarrow\begin{cases}\dfrac{-3}{2} = y + 4\\x = \dfrac{-3}{2}\end{cases}\Leftrightarrow\begin{cases}y = \dfrac{-11}{2}\\x = \dfrac{-3}{2}\end{cases}\\b) \begin{cases}2x + y = 7\\3y - x = 7\end{cases}\Leftrightarrow\begin{cases}2x + y = 7\\6y - 2x = 14\end{cases}\Leftrightarrow\begin{cases}2x + y = 7\\7y = 21\end{cases}\Leftrightarrow\begin{cases}2x + 3 = 7\\y = 3\end{cases}\Leftrightarrow\begin{cases}x=2\\y=3\end{cases}\\ c) \begin{cases} 5x + y = 3 \\ -x - \dfrac{1}{5}y=\dfrac{-3}{5} \end{cases} \Leftrightarrow \begin{cases} 5x + y = 3 \\ 5x + y = 3 \end{cases} (luôn\ đúng) \Leftrightarrow Phương\ trình\ vô\ số\ nghiệm \\d) \begin{cases} 3x - 5y = -18 \\ x - 5 = 2y \end{cases} \Leftrightarrow \begin{cases} 3x - 5y = -18 \\ 3x - 6y = 15 \end{cases} \Leftrightarrow \begin{cases} x - 5 = 2.(-33)\\ y = -13 \end{cases} \Leftrightarrow \begin{cases}x = -61\\y=-33 \end{cases} \)

a)\(\left\{{}\begin{matrix}-2y=-6\\x-5y=16\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}y=3\\x=16+5y\end{matrix}\right.\Leftrightarrow}\left\{{}\begin{matrix}y=3\\x=31\end{matrix}\right.\)

b)\(\left\{{}\begin{matrix}2x+y=7\\-2x+8y=20\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}9y=27\\-2x+8y=20\end{matrix}\right.\Leftrightarrow}\left\{{}\begin{matrix}y=3\\-2x=20-8y\end{matrix}\right.\Leftrightarrow}\left\{{}\begin{matrix}y=3\\x=2\end{matrix}\right.\)

a)\(\left\{{}\begin{matrix}-x+3y=10\\x-5y=16\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}-2y=26\\x-5y=16\end{matrix}\right.\Leftrightarrow}\left\{{}\begin{matrix}y=-13\\x-5.\left(-13\right)=16\end{matrix}\right.\Leftrightarrow}\left\{{}\begin{matrix}y=-13\\x=-49\end{matrix}\right.\)

mấy bài này là ở lớp 9 học kì 2 dùng cộng đại số là nhanh nhất hoặc bấm máy tính

Coi PT thứ nhất là PT(1) và PT thứ 2 là PT(2)

a)

Từ PT$(2)\Rightarrow y=18-5x$

Thế vào PT$(1)$: $3x-2(18-5x)=5$

$\Leftrightarrow 13x=41\Leftrightarrow x=\frac{41}{13}$

\(y=18-5x=18-5.\frac{41}{13}=\frac{29}{13}\)

Vậy.......

b)

PT\((1)\Rightarrow y=2x-8\)

Thế vào $PT(2)\Rightarrow$ \(x+3(2x-8)=10\)

$\Leftrightarrow 7x=34\Rightarrow x=\frac{34}{7}$

$y=2x-8=2.\frac{34}{7}-8=\frac{12}{7}$

Vậy........

c)

HPT \(\Leftrightarrow \left\{\begin{matrix} 12x-9y=6\\ 12x-16y=-8\end{matrix}\right.\)

Từ PT$(1)\Rightarrow 12x=9y+6$

Thế vào PT$(2)\Rightarrow 9y+6-16y=-8$

$\Leftrightarrow y=2$

$x=\frac{9y+6}{12}=\frac{9.2+6}{12}=2$

Vậy.........

d)

HPT \(\Leftrightarrow \left\{\begin{matrix} 10x+25y=65\\ 10x-6y=-28\end{matrix}\right.\)

Từ PT$(1)\Rightarrow 10x=65-25y$

Thế vào PT$(2)\Rightarrow 65-25y-6y=-28$

$\Leftrightarrow y=3$

$x=\frac{65-25y}{10}=\frac{65-25.3}{10}=-1$

Vậy........

Câu 1: 

Lấy PT(1) + PT(2) theo vế thu được:

$3x+y+(2x-y)=10$

$\Leftrightarrow 5x=10$

$\Leftrightarrow x=2$

$y=2x-7=2.2-7=-3$

Vậy hpt có nghiệm $(x,y)=(2,-3)$

Câu 2: 

Lấy PT(1) - PT(2) theo vế thì:

$(2x+5y)-(2x-3y)=8$

$\Leftrightarrow 8y=8$

$\Leftrightarrow y=1$

Khi đó: $x=3y:2=\frac{3}{2}$
Vậy.............

Câu 3:

Lấy PT(1) - 2PT(2) thu được:

$(4x+3y)-2(2x+y)=6-2.4$

$\Leftrightarrow y=-2$

Khi đó:

$2x=4-y=6$

$\Leftrightarrow x=3$

Vậy..........