Aftrekken geeft \(-p = 10 \text{,}\) dus \(p = -10 \text{.}\)

\(\begin{rcases}5 p - 5 q = 5 \\ p = -10\end{rcases} \begin{matrix}5 ⋅ -10 - 5 q = 5 \\ -5 q = 55 \\ q = -11\end{matrix}\)

De oplossing is \((p , q) = (-10 , -11) \text{.}\)

\(\begin{cases}5 a + b = 6 \\ 6 a + 2 b = -4\end{cases}\) \(\begin{vmatrix}2 \\ 1\end{vmatrix}\) geeft \(\begin{cases}10 a + 2 b = 12 \\ 6 a + 2 b = -4\end{cases}\)

Aftrekken geeft \(4 a = 16 \text{,}\) dus \(a = 4 \text{.}\)

\(\begin{rcases}5 a + b = 6 \\ a = 4\end{rcases} \begin{matrix}5 ⋅ 4 + b = 6 \\ b = -14\end{matrix}\)

De oplossing is \((a , b) = (4 , -14) \text{.}\)

\(\begin{cases}6 a + 2 b = -6 \\ 5 a - 3 b = 2\end{cases}\) \(\begin{vmatrix}3 \\ 2\end{vmatrix}\) geeft \(\begin{cases}18 a + 6 b = -18 \\ 10 a - 6 b = 4\end{cases}\)

Optellen geeft \(28 a = -14 \text{,}\) dus \(a = -\frac{1}{2} \text{.}\)

\(\begin{rcases}6 a + 2 b = -6 \\ a = -\frac{1}{2}\end{rcases} \begin{matrix}6 ⋅ -\frac{1}{2} + 2 b = -6 \\ 2 b = -3 \\ b = -1\frac{1}{2}\end{matrix}\)

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

Gelijk stellen geeft \(8 x + 44 = 2 x + 14\)

\(6 x = -30\) dus \(x = -5\)

\(\begin{rcases}y = 8 x + 44 \\ x = -5\end{rcases} \begin{matrix}y = 8 ⋅ -5 + 44 \\ y = 4\end{matrix}\)

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

Substitutie geeft \(7 (9 y + 52) + 3 y = -32\)

Haakjes wegwerken geeft
\(63 y + 364 + 3 y = -32\)
\(66 y = -396\)
\(y = -6\)

\(\begin{rcases}x = 9 y + 52 \\ y = -6\end{rcases} \begin{matrix}x = 9 ⋅ -6 + 52 \\ x = -2\end{matrix}\)

De oplossing is \((x , y) = (-2 , -6) \text{.}\)

Substitutie geeft \(x = 9 (2 x + 5) - 11\)

Haakjes wegwerken geeft
\(x = 18 x + 45 - 11\)
\(-17 x = 34\)
\(x = -2\)

\(\begin{rcases}y = 2 x + 5 \\ x = -2\end{rcases} \begin{matrix}y = 2 ⋅ -2 + 5 \\ y = 1\end{matrix}\)

De oplossing is \((x , y) = (-2 , 1) \text{.}\)