Aftrekken geeft \(y = -6 \text{.}\)

\(\begin{rcases}3 x + 2 y = -3 \\ y = -6\end{rcases} \begin{matrix}3 x + 2 ⋅ -6 = -3 \\ 3 x = 9 \\ x = 3\end{matrix}\)

De oplossing is \((x , y) = (3 , -6) \text{.}\)

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

Optellen geeft \(8 a = 16 \text{,}\) dus \(a = 2 \text{.}\)

\(\begin{rcases}a - b = 6 \\ a = 2\end{rcases} \begin{matrix}2 - b = 6 \\ -b = 4 \\ b = -4\end{matrix}\)

De oplossing is \((a , b) = (2 , -4) \text{.}\)

\(\begin{cases}5 x - 3 y = -6 \\ 3 x - 5 y = -2\end{cases}\) \(\begin{vmatrix}5 \\ 3\end{vmatrix}\) geeft \(\begin{cases}25 x - 15 y = -30 \\ 9 x - 15 y = -6\end{cases}\)

Aftrekken geeft \(16 x = -24 \text{,}\) dus \(x = -1\frac{1}{2} \text{.}\)

\(\begin{rcases}5 x - 3 y = -6 \\ x = -1\frac{1}{2}\end{rcases} \begin{matrix}5 ⋅ -1\frac{1}{2} - 3 y = -6 \\ -3 y = 1\frac{1}{2} \\ y = -\frac{1}{2}\end{matrix}\)

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

Gelijk stellen geeft \(4 y + 21 = 9 y + 41\)

\(-5 y = 20\) dus \(y = -4\)

\(\begin{rcases}x = 4 y + 21 \\ y = -4\end{rcases} \begin{matrix}x = 4 ⋅ -4 + 21 \\ x = 5\end{matrix}\)

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

Substitutie geeft \(5 (3 b + 11) + 7 b = 11\)

Haakjes wegwerken geeft
\(15 b + 55 + 7 b = 11\)
\(22 b = -44\)
\(b = -2\)

\(\begin{rcases}a = 3 b + 11 \\ b = -2\end{rcases} \begin{matrix}a = 3 ⋅ -2 + 11 \\ a = 5\end{matrix}\)

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

Substitutie geeft \(p = 3 (6 p - 8) - 10\)

Haakjes wegwerken geeft
\(p = 18 p - 24 - 10\)
\(-17 p = -34\)
\(p = 2\)

\(\begin{rcases}q = 6 p - 8 \\ p = 2\end{rcases} \begin{matrix}q = 6 ⋅ 2 - 8 \\ q = 4\end{matrix}\)

De oplossing is \((p , q) = (2 , 4) \text{.}\)