Jeśli rozwiązaniem układu jest para liczb (5, -3), to możemy podstawić 5 w miejsce x oraz -3 w miejsce y. 

$a)$

$\{\begin{array}{l}m\cdot 5-\left(-3\right)=23\\ n\cdot 5+\left(-3\right)=12\end{array}$

$\{\begin{array}{l}5m+3=23\mid -3\\ 5n-3=12\mid +3\end{array}$

$\{\begin{array}{l}5m=20\mid :5\\ 5n=15\mid :5\end{array}$

$\{\begin{array}{l}m=4\\ n=3\end{array}$

 

$b)$

$\{\begin{array}{l}m\cdot 5+n\cdot \left(-3\right)=12\\ m\cdot 5-n\cdot \left(-3\right)=18\end{array}$

$\{\begin{array}{l}5m-3n=12\\ 5m+3n=18\end{array}\mid +$

$10m=30\mid :10$

$m=3$

 

$\{\begin{array}{l}m=3\\ 5m-3n=12\end{array}$

$\{\begin{array}{l}m=3\\ 5\cdot 3-3n=12\end{array}$

$\{\begin{array}{l}m=3\\ 15-3n=12\mid -15\end{array}$

$\{\begin{array}{l}m=3\\ -3n=-3\mid :\left(-3\right)\end{array}$

$\{\begin{array}{l}9m=3\\ n=1\end{array}$

 

$c)$

$\{\begin{array}{l}m\cdot 5+n\cdot \left(-3\right)=-11\\ 2\cdot m\cdot 5-3\cdot n\cdot \left(-3\right)=8\end{array}$

$\{\begin{array}{l}5m-3n=-11\mid \cdot 3\\ 10m+9n=8\end{array}$

$\{\begin{array}{l}15m-9n=-33\\ 10m+9n=8\end{array}\mid +$

$25m=-25\mid :25$

$m=-1$

 

$\{\begin{array}{l}m=-1\\ 5m-3n=-11\end{array}$

$\{\begin{array}{l}m=-1\\ 5\cdot \left(-1\right)-3n=-11\end{array}$

$\{\begin{array}{l}m=-1\\ -5-3n=-11\mid +5\end{array}$

$\{\begin{array}{l}m=-1\\ -3n=-6\mid :\left(-3\right)\end{array}$

$\{\begin{array}{l}m=-1\\ n=2\end{array}$