Question

Tìm x, y

a, xy+3x-7y=21

b, xy+3x-2y=11

Answer 1

a) \(xy+3x-7y=21\)

\(\Leftrightarrow x\left(y+3\right)-7y-21=0\)

\(\Leftrightarrow x\left(y+3\right)-7\left(y+3\right)=0\)

\(\Leftrightarrow\left(x-7\right)\left(y+3\right)=0\)

\(\Leftrightarrow\hept{\begin{cases}x-7=0\\y+3=0\end{cases}}\Leftrightarrow\hept{\begin{cases}x=7\\y=-3\end{cases}}\)

Vậy x = 7 và y = -3

Answer 2

b) \(xy+3x-2y=11\)

\(\Leftrightarrow x\left(y+3\right)-2y-6=5\)

\(\Leftrightarrow x\left(y+3\right)-2\left(y+3\right)=5\)

\(\Leftrightarrow\left(x-2\right)\left(y+3\right)=5=1.5=5.1=\left(-1\right).\left(-5\right)=\left(-5\right).\left(-1\right)\)

Lập bảng:

\(x-2\)	\(1\)	\(5\)	\(-1\)	\(-5\)
\(y+3\)	\(5\)	\(1\)	\(-5\)	\(-1\)
\(x\)	\(3\)	\(7\)	\(1\)	\(-3\)
\(y\)	\(2\)	\(-2\)	\(-8\)	\(-4\)

Vậy \(\left(x,y\right)\in\left\{\left(3,2\right);\left(7,-2\right);\left(1,-8\right);\left(-3,-3\right)\right\}\)