Optellen geeft \(5 a = -10 \text{,}\) dus \(a = -2 \text{.}\)

\(\begin{rcases}4 a - 6 b = -5 \\ a = -2\end{rcases} \begin{matrix}4 ⋅ -2 - 6 b = -5 \\ -6 b = 3 \\ b = -\frac{1}{2}\end{matrix}\)

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

\(\begin{cases}6 x + 3 y = -3 \\ 3 x + y = 1\end{cases}\) \(\begin{vmatrix}1 \\ 3\end{vmatrix}\) geeft \(\begin{cases}6 x + 3 y = -3 \\ 9 x + 3 y = 3\end{cases}\)

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

\(\begin{rcases}6 x + 3 y = -3 \\ x = 2\end{rcases} \begin{matrix}6 ⋅ 2 + 3 y = -3 \\ 3 y = -15 \\ y = -5\end{matrix}\)

De oplossing is \((x , y) = (2 , -5) \text{.}\)

\(\begin{cases}3 p - 4 q = -5 \\ 4 p - 3 q = 5\end{cases}\) \(\begin{vmatrix}3 \\ 4\end{vmatrix}\) geeft \(\begin{cases}9 p - 12 q = -15 \\ 16 p - 12 q = 20\end{cases}\)

Aftrekken geeft \(-7 p = -35 \text{,}\) dus \(p = 5 \text{.}\)

\(\begin{rcases}3 p - 4 q = -5 \\ p = 5\end{rcases} \begin{matrix}3 ⋅ 5 - 4 q = -5 \\ -4 q = -20 \\ q = 5\end{matrix}\)

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

Gelijk stellen geeft \(5 x + 26 = 7 x + 36\)

\(-2 x = 10\) dus \(x = -5\)

\(\begin{rcases}y = 5 x + 26 \\ x = -5\end{rcases} \begin{matrix}y = 5 ⋅ -5 + 26 \\ y = 1\end{matrix}\)

De oplossing is \((x , y) = (-5 , 1) \text{.}\)

Substitutie geeft \(4 a + 9 (6 a + 24) = -74\)

Haakjes wegwerken geeft
\(4 a + 54 a + 216 = -74\)
\(58 a = -290\)
\(a = -5\)

\(\begin{rcases}b = 6 a + 24 \\ a = -5\end{rcases} \begin{matrix}b = 6 ⋅ -5 + 24 \\ b = -6\end{matrix}\)

De oplossing is \((a , b) = (-5 , -6) \text{.}\)

Substitutie geeft \(x = 8 (6 x - 27) - 19\)

Haakjes wegwerken geeft
\(x = 48 x - 216 - 19\)
\(-47 x = -235\)
\(x = 5\)

\(\begin{rcases}y = 6 x - 27 \\ x = 5\end{rcases} \begin{matrix}y = 6 ⋅ 5 - 27 \\ y = 3\end{matrix}\)

De oplossing is \((x , y) = (5 , 3) \text{.}\)