Optellen geeft \(8 a = -4 \text{,}\) dus \(a = -\frac{1}{2} \text{.}\)

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

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

\(\begin{cases}6 a - 4 b = 4 \\ 4 a - b = -4\end{cases}\) \(\begin{vmatrix}1 \\ 4\end{vmatrix}\) geeft \(\begin{cases}6 a - 4 b = 4 \\ 16 a - 4 b = -16\end{cases}\)

Aftrekken geeft \(-10 a = 20 \text{,}\) dus \(a = -2 \text{.}\)

\(\begin{rcases}6 a - 4 b = 4 \\ a = -2\end{rcases} \begin{matrix}6 ⋅ -2 - 4 b = 4 \\ -4 b = 16 \\ b = -4\end{matrix}\)

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

\(\begin{cases}3 x + 5 y = -2 \\ 2 x + 4 y = 4\end{cases}\) \(\begin{vmatrix}4 \\ 5\end{vmatrix}\) geeft \(\begin{cases}12 x + 20 y = -8 \\ 10 x + 20 y = 20\end{cases}\)

Aftrekken geeft \(2 x = -28 \text{,}\) dus \(x = -14 \text{.}\)

\(\begin{rcases}3 x + 5 y = -2 \\ x = -14\end{rcases} \begin{matrix}3 ⋅ -14 + 5 y = -2 \\ 5 y = 40 \\ y = 8\end{matrix}\)

De oplossing is \((x , y) = (-14 , 8) \text{.}\)

Gelijk stellen geeft \(2 x + 7 = 5 x + 13\)

\(-3 x = 6\) dus \(x = -2\)

\(\begin{rcases}y = 2 x + 7 \\ x = -2\end{rcases} \begin{matrix}y = 2 ⋅ -2 + 7 \\ y = 3\end{matrix}\)

De oplossing is \((x , y) = (-2 , 3) \text{.}\)

Substitutie geeft \(8 (6 y - 7) + 3 y = 46\)

Haakjes wegwerken geeft
\(48 y - 56 + 3 y = 46\)
\(51 y = 102\)
\(y = 2\)

\(\begin{rcases}x = 6 y - 7 \\ y = 2\end{rcases} \begin{matrix}x = 6 ⋅ 2 - 7 \\ x = 5\end{matrix}\)

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

Substitutie geeft \(q = 8 (2 q + 14) - 37\)

Haakjes wegwerken geeft
\(q = 16 q + 112 - 37\)
\(-15 q = 75\)
\(q = -5\)

\(\begin{rcases}p = 2 q + 14 \\ q = -5\end{rcases} \begin{matrix}p = 2 ⋅ -5 + 14 \\ p = 4\end{matrix}\)

De oplossing is \((p , q) = (4 , -5) \text{.}\)