Aftrekken geeft \(3 x = -9 \text{,}\) dus \(x = -3 \text{.}\)

\(\begin{rcases}5 x + 3 y = -6 \\ x = -3\end{rcases} \begin{matrix}5 ⋅ -3 + 3 y = -6 \\ 3 y = 9 \\ y = 3\end{matrix}\)

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

\(\begin{cases}2 p - 4 q = 3 \\ 3 p + q = 1\end{cases}\) \(\begin{vmatrix}1 \\ 4\end{vmatrix}\) geeft \(\begin{cases}2 p - 4 q = 3 \\ 12 p + 4 q = 4\end{cases}\)

Optellen geeft \(14 p = 7 \text{,}\) dus \(p = \frac{1}{2} \text{.}\)

\(\begin{rcases}2 p - 4 q = 3 \\ p = \frac{1}{2}\end{rcases} \begin{matrix}2 ⋅ \frac{1}{2} - 4 q = 3 \\ -4 q = 2 \\ q = -\frac{1}{2}\end{matrix}\)

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

\(\begin{cases}6 a - 4 b = -4 \\ 5 a - 3 b = -6\end{cases}\) \(\begin{vmatrix}3 \\ 4\end{vmatrix}\) geeft \(\begin{cases}18 a - 12 b = -12 \\ 20 a - 12 b = -24\end{cases}\)

Aftrekken geeft \(-2 a = 12 \text{,}\) dus \(a = -6 \text{.}\)

\(\begin{rcases}6 a - 4 b = -4 \\ a = -6\end{rcases} \begin{matrix}6 ⋅ -6 - 4 b = -4 \\ -4 b = 32 \\ b = -8\end{matrix}\)

De oplossing is \((a , b) = (-6 , -8) \text{.}\)

Gelijk stellen geeft \(4 y = 9 y + 5\)

\(-5 y = 5\) dus \(y = -1\)

\(\begin{rcases}x = 4 y \\ y = -1\end{rcases} \begin{matrix}x = 4 ⋅ -1 + 0 \\ x = -4\end{matrix}\)

De oplossing is \((x , y) = (-4 , -1) \text{.}\)

Substitutie geeft \(4 (3 b - 18) + 6 b = 18\)

Haakjes wegwerken geeft
\(12 b - 72 + 6 b = 18\)
\(18 b = 90\)
\(b = 5\)

\(\begin{rcases}a = 3 b - 18 \\ b = 5\end{rcases} \begin{matrix}a = 3 ⋅ 5 - 18 \\ a = -3\end{matrix}\)

De oplossing is \((a , b) = (-3 , 5) \text{.}\)

Substitutie geeft \(x = 4 (9 x + 26) + 1\)

Haakjes wegwerken geeft
\(x = 36 x + 104 + 1\)
\(-35 x = 105\)
\(x = -3\)

\(\begin{rcases}y = 9 x + 26 \\ x = -3\end{rcases} \begin{matrix}y = 9 ⋅ -3 + 26 \\ y = -1\end{matrix}\)

De oplossing is \((x , y) = (-3 , -1) \text{.}\)