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

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

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

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

Aftrekken geeft \(4 a = 6 \text{,}\) dus \(a = 1\frac{1}{2} \text{.}\)

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

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

\(\begin{cases}5 p + 3 q = -4 \\ 3 p + 2 q = -4\end{cases}\) \(\begin{vmatrix}2 \\ 3\end{vmatrix}\) geeft \(\begin{cases}10 p + 6 q = -8 \\ 9 p + 6 q = -12\end{cases}\)

Aftrekken geeft \(p = 4 \text{.}\)

\(\begin{rcases}5 p + 3 q = -4 \\ p = 4\end{rcases} \begin{matrix}5 ⋅ 4 + 3 q = -4 \\ 3 q = -24 \\ q = -8\end{matrix}\)

De oplossing is \((p , q) = (4 , -8) \text{.}\)

Gelijk stellen geeft \(3 x - 2 = 7 x + 2\)

\(-4 x = 4\) dus \(x = -1\)

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

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

Substitutie geeft \(2 (7 y - 10) + 3 y = -3\)

Haakjes wegwerken geeft
\(14 y - 20 + 3 y = -3\)
\(17 y = 17\)
\(y = 1\)

\(\begin{rcases}x = 7 y - 10 \\ y = 1\end{rcases} \begin{matrix}x = 7 ⋅ 1 - 10 \\ x = -3\end{matrix}\)

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

Substitutie geeft \(y = 9 (4 y + 2) - 53\)

Haakjes wegwerken geeft
\(y = 36 y + 18 - 53\)
\(-35 y = -35\)
\(y = 1\)

\(\begin{rcases}x = 4 y + 2 \\ y = 1\end{rcases} \begin{matrix}x = 4 ⋅ 1 + 2 \\ x = 6\end{matrix}\)

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