Question

Biết hệ phương trình

5 - 2(x + y) = - 3y;

x - 1 = 2y + 3

. Tính giá trị củabiểu thức T = 2025x_{o} - 2026y_{o} có nghiệm (x_{o}; y_{o}) duy nhất. 

Answer 1

\(\left\{{}\begin{matrix}5-2\left(x+y\right)=-3y\\x-1=2y+3\end{matrix}\right.\)

=>\(\left\{{}\begin{matrix}-3y+2\left(x+y\right)=5\\x-2y=4\end{matrix}\right.\)

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

=>\(\left\{{}\begin{matrix}2x-y=5\\2x-4y=8\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}2x-y-2x+4y=5-8\\x-2y=4\end{matrix}\right.\)

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

\(T=2025\cdot x_0-2026\cdot y_0\)

\(=2025\cdot2-2026\cdot\left(-1\right)\)

=4050+2026

=6076