Aftrekken geeft \(3 y = -6 \text{,}\) dus \(y = -2 \text{.}\)

\(\begin{rcases}3 x - 3 y = -3 \\ y = -2\end{rcases} \begin{matrix}3 x - 3 ⋅ -2 = -3 \\ 3 x = -9 \\ x = -3\end{matrix}\)

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

\(\begin{cases}2 a + 2 b = -4 \\ 6 a - 6 b = -6\end{cases}\) \(\begin{vmatrix}3 \\ 1\end{vmatrix}\) geeft \(\begin{cases}6 a + 6 b = -12 \\ 6 a - 6 b = -6\end{cases}\)

Optellen geeft \(12 a = -18 \text{,}\) dus \(a = -1\frac{1}{2} \text{.}\)

\(\begin{rcases}2 a + 2 b = -4 \\ a = -1\frac{1}{2}\end{rcases} \begin{matrix}2 ⋅ -1\frac{1}{2} + 2 b = -4 \\ 2 b = -1 \\ b = -\frac{1}{2}\end{matrix}\)

De oplossing is \((a , b) = (-1\frac{1}{2} , -\frac{1}{2}) \text{.}\)

\(\begin{cases}5 a - 6 b = -5 \\ 3 a - 4 b = 5\end{cases}\) \(\begin{vmatrix}2 \\ 3\end{vmatrix}\) geeft \(\begin{cases}10 a - 12 b = -10 \\ 9 a - 12 b = 15\end{cases}\)

Aftrekken geeft \(a = -25 \text{.}\)

\(\begin{rcases}5 a - 6 b = -5 \\ a = -25\end{rcases} \begin{matrix}5 ⋅ -25 - 6 b = -5 \\ -6 b = 120 \\ b = -20\end{matrix}\)

De oplossing is \((a , b) = (-25 , -20) \text{.}\)

Gelijk stellen geeft \(7 y + 23 = 5 y + 15\)

\(2 y = -8\) dus \(y = -4\)

\(\begin{rcases}x = 7 y + 23 \\ y = -4\end{rcases} \begin{matrix}x = 7 ⋅ -4 + 23 \\ x = -5\end{matrix}\)

De oplossing is \((x , y) = (-5 , -4) \text{.}\)

Substitutie geeft \(8 (2 y - 3) + 7 y = 68\)

Haakjes wegwerken geeft
\(16 y - 24 + 7 y = 68\)
\(23 y = 92\)
\(y = 4\)

\(\begin{rcases}x = 2 y - 3 \\ y = 4\end{rcases} \begin{matrix}x = 2 ⋅ 4 - 3 \\ x = 5\end{matrix}\)

De oplossing is \((x , y) = (5 , 4) \text{.}\)

Substitutie geeft \(q = 6 (9 q + 22) + 27\)

Haakjes wegwerken geeft
\(q = 54 q + 132 + 27\)
\(-53 q = 159\)
\(q = -3\)

\(\begin{rcases}p = 9 q + 22 \\ q = -3\end{rcases} \begin{matrix}p = 9 ⋅ -3 + 22 \\ p = -5\end{matrix}\)

De oplossing is \((p , q) = (-5 , -3) \text{.}\)