Question

Giải các hệ phương trình sau:
a.{ x + 4y = -11
   { 5x - 4y = 1
b.{ 2x - y = 7
   { 3x + 5y + 22 = 0
c.{ 2(x - 2) + 3(1 + y) = 2
   { 3(x - 2) - 2(1 + y) = -3
d.{ (x - 5)(y - 2) = (x + 2)(y - 1)
   { (x - 4)(y + 7) = (x - 3)(y + 4)
e.{ 1/x - 1/y = 1
   { 3/x + 4/y = 5

Answer 1

a: \(\left\{{}\begin{matrix}x+4y=-11\\5x-4y=1\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}6x=-10\\x+4y=-11\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{-5}{3}\\y=\dfrac{-11-x}{4}=\dfrac{-11+\dfrac{5}{3}}{4}=-\dfrac{7}{3}\end{matrix}\right.\)

b: \(\left\{{}\begin{matrix}2x-y=7\\3x+5y=-22\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}6x-3y=21\\6x+15y=-66\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}-18y=78\\2x-y=7\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}y=\dfrac{-13}{3}\\x=\dfrac{y+7}{2}=\dfrac{4}{3}\end{matrix}\right.\)