Aftrekken geeft \(-x = 12 \text{,}\) dus \(x = -12 \text{.}\)

\(\begin{rcases}x - 6 y = 6 \\ x = -12\end{rcases} \begin{matrix}-12 - 6 y = 6 \\ -6 y = 18 \\ y = -3\end{matrix}\)

De oplossing is \((x , y) = (-12 , -3) \text{.}\)

\(\begin{cases}x - y = -5 \\ 6 x + 6 y = 6\end{cases}\) \(\begin{vmatrix}6 \\ 1\end{vmatrix}\) geeft \(\begin{cases}6 x - 6 y = -30 \\ 6 x + 6 y = 6\end{cases}\)

Optellen geeft \(12 x = -24 \text{,}\) dus \(x = -2 \text{.}\)

\(\begin{rcases}x - y = -5 \\ x = -2\end{rcases} \begin{matrix}-2 - y = -5 \\ -y = -3 \\ y = 3\end{matrix}\)

De oplossing is \((x , y) = (-2 , 3) \text{.}\)

\(\begin{cases}5 a + 3 b = 4 \\ 3 a + 4 b = -2\end{cases}\) \(\begin{vmatrix}4 \\ 3\end{vmatrix}\) geeft \(\begin{cases}20 a + 12 b = 16 \\ 9 a + 12 b = -6\end{cases}\)

Aftrekken geeft \(11 a = 22 \text{,}\) dus \(a = 2 \text{.}\)

\(\begin{rcases}5 a + 3 b = 4 \\ a = 2\end{rcases} \begin{matrix}5 ⋅ 2 + 3 b = 4 \\ 3 b = -6 \\ b = -2\end{matrix}\)

De oplossing is \((a , b) = (2 , -2) \text{.}\)

Gelijk stellen geeft \(5 y + 23 = 2 y + 11\)

\(3 y = -12\) dus \(y = -4\)

\(\begin{rcases}x = 5 y + 23 \\ y = -4\end{rcases} \begin{matrix}x = 5 ⋅ -4 + 23 \\ x = 3\end{matrix}\)

De oplossing is \((x , y) = (3 , -4) \text{.}\)

Substitutie geeft \(2 (4 q - 19) + 7 q = 37\)

Haakjes wegwerken geeft
\(8 q - 38 + 7 q = 37\)
\(15 q = 75\)
\(q = 5\)

\(\begin{rcases}p = 4 q - 19 \\ q = 5\end{rcases} \begin{matrix}p = 4 ⋅ 5 - 19 \\ p = 1\end{matrix}\)

De oplossing is \((p , q) = (1 , 5) \text{.}\)

Substitutie geeft \(a = 5 (7 a + 29) - 9\)

Haakjes wegwerken geeft
\(a = 35 a + 145 - 9\)
\(-34 a = 136\)
\(a = -4\)

\(\begin{rcases}b = 7 a + 29 \\ a = -4\end{rcases} \begin{matrix}b = 7 ⋅ -4 + 29 \\ b = 1\end{matrix}\)

De oplossing is \((a , b) = (-4 , 1) \text{.}\)