Aftrekken geeft \(-2 y = -5 \text{,}\) dus \(y = 2\frac{1}{2} \text{.}\)

\(\begin{rcases}2 x - 6 y = -2 \\ y = 2\frac{1}{2}\end{rcases} \begin{matrix}2 x - 6 ⋅ 2\frac{1}{2} = -2 \\ 2 x = 13 \\ x = 6\frac{1}{2}\end{matrix}\)

De oplossing is \((x , y) = (6\frac{1}{2} , 2\frac{1}{2}) \text{.}\)

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

Aftrekken geeft \(a = -9 \text{.}\)

\(\begin{rcases}5 a - 2 b = 1 \\ a = -9\end{rcases} \begin{matrix}5 ⋅ -9 - 2 b = 1 \\ -2 b = 46 \\ b = -23\end{matrix}\)

De oplossing is \((a , b) = (-9 , -23) \text{.}\)

\(\begin{cases}2 x + 4 y = 3 \\ 5 x - 3 y = 1\end{cases}\) \(\begin{vmatrix}3 \\ 4\end{vmatrix}\) geeft \(\begin{cases}6 x + 12 y = 9 \\ 20 x - 12 y = 4\end{cases}\)

Optellen geeft \(26 x = 13 \text{,}\) dus \(x = \frac{1}{2} \text{.}\)

\(\begin{rcases}2 x + 4 y = 3 \\ x = \frac{1}{2}\end{rcases} \begin{matrix}2 ⋅ \frac{1}{2} + 4 y = 3 \\ 4 y = 2 \\ y = \frac{1}{2}\end{matrix}\)

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

Gelijk stellen geeft \(8 y - 18 = 4 y - 10\)

\(4 y = 8\) dus \(y = 2\)

\(\begin{rcases}x = 8 y - 18 \\ y = 2\end{rcases} \begin{matrix}x = 8 ⋅ 2 - 18 \\ x = -2\end{matrix}\)

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

Substitutie geeft \(3 (4 q + 1) + 7 q = 22\)

Haakjes wegwerken geeft
\(12 q + 3 + 7 q = 22\)
\(19 q = 19\)
\(q = 1\)

\(\begin{rcases}p = 4 q + 1 \\ q = 1\end{rcases} \begin{matrix}p = 4 ⋅ 1 + 1 \\ p = 5\end{matrix}\)

De oplossing is \((p , q) = (5 , 1) \text{.}\)

Substitutie geeft \(b = 4 (2 b + 4) + 19\)

Haakjes wegwerken geeft
\(b = 8 b + 16 + 19\)
\(-7 b = 35\)
\(b = -5\)

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

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