\(\left\{{}\begin{matrix}5x+2y=8\\2x+3y=9\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}-3\left(5x+2y\right)=\left(-3\right).8\\2\left(2x+3y\right)=2.9\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}-15x-6y=-24\\4x+6y=18\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}-11x=-6\\5x+2y=8\end{matrix}\right.\)\(\Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{6}{11}\\5.\dfrac{6}{11}+2y=8\end{matrix}\right.\)\(\Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{6}{11}\\y=\dfrac{29}{11}\end{matrix}\right.\)
Vậy nghiệm của hệ phương trình là\(\left\{{}\begin{matrix}x=\dfrac{6}{11}\\y=\dfrac{29}{11}\end{matrix}\right.\)
ta sẽ có \(\left\{{}\begin{matrix}5x+2y=8\\2x+3y=9\end{matrix}\right.\)
<=> \(\left\{{}\begin{matrix}3.\left(5x+2y\right)=8.3\\2.\left(2x+3y\right)=9.2\end{matrix}\right.\)
<=> \(\left\{{}\begin{matrix}15x+6y=24\\4x+6y=18\end{matrix}\right.\)
<=> \(\left\{{}\begin{matrix}11x=6\\4x+6y=18\end{matrix}\right.\)
<=> \(\left\{{}\begin{matrix}x=\dfrac{6}{11}\\y=\dfrac{18-4.\dfrac{6}{11}}{6}\end{matrix}\right.\)
<=> \(\left\{{}\begin{matrix}x=\dfrac{6}{11}\\y=\dfrac{29}{11}\end{matrix}\right.\)
vậy hệ phương trình có nghiệm là \(\left\{\dfrac{6}{11};\dfrac{29}{11}\right\}\)
