Aftrekken geeft \(-2 p = -4 \text{,}\) dus \(p = 2 \text{.}\)

\(\begin{rcases}2 p - q = -1 \\ p = 2\end{rcases} \begin{matrix}2 ⋅ 2 - q = -1 \\ -q = -5 \\ q = 5\end{matrix}\)

De oplossing is \((p , q) = (2 , 5) \text{.}\)

\(\begin{cases}2 x - y = -6 \\ x + 4 y = 6\end{cases}\) \(\begin{vmatrix}4 \\ 1\end{vmatrix}\) geeft \(\begin{cases}8 x - 4 y = -24 \\ x + 4 y = 6\end{cases}\)

Optellen geeft \(9 x = -18 \text{,}\) dus \(x = -2 \text{.}\)

\(\begin{rcases}2 x - y = -6 \\ x = -2\end{rcases} \begin{matrix}2 ⋅ -2 - y = -6 \\ -y = -2 \\ y = 2\end{matrix}\)

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

\(\begin{cases}3 a + 5 b = 4 \\ 4 a + 3 b = -2\end{cases}\) \(\begin{vmatrix}3 \\ 5\end{vmatrix}\) geeft \(\begin{cases}9 a + 15 b = 12 \\ 20 a + 15 b = -10\end{cases}\)

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

\(\begin{rcases}3 a + 5 b = 4 \\ a = -2\end{rcases} \begin{matrix}3 ⋅ -2 + 5 b = 4 \\ 5 b = 10 \\ b = 2\end{matrix}\)

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

Gelijk stellen geeft \(9 y + 33 = 7 y + 25\)

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

\(\begin{rcases}x = 9 y + 33 \\ y = -4\end{rcases} \begin{matrix}x = 9 ⋅ -4 + 33 \\ x = -3\end{matrix}\)

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

Substitutie geeft \(8 (9 y - 34) + 4 y = 32\)

Haakjes wegwerken geeft
\(72 y - 272 + 4 y = 32\)
\(76 y = 304\)
\(y = 4\)

\(\begin{rcases}x = 9 y - 34 \\ y = 4\end{rcases} \begin{matrix}x = 9 ⋅ 4 - 34 \\ x = 2\end{matrix}\)

De oplossing is \((x , y) = (2 , 4) \text{.}\)

Substitutie geeft \(b = 5 (9 b + 23) - 27\)

Haakjes wegwerken geeft
\(b = 45 b + 115 - 27\)
\(-44 b = 88\)
\(b = -2\)

\(\begin{rcases}a = 9 b + 23 \\ b = -2\end{rcases} \begin{matrix}a = 9 ⋅ -2 + 23 \\ a = 5\end{matrix}\)

De oplossing is \((a , b) = (5 , -2) \text{.}\)