Optellen geeft \(6 a = 9 \text{,}\) dus \(a = 1\frac{1}{2} \text{.}\)

\(\begin{rcases}a + b = 4 \\ a = 1\frac{1}{2}\end{rcases} \begin{matrix}1\frac{1}{2} + b = 4 \\ b = 2\frac{1}{2}\end{matrix}\)

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

\(\begin{cases}3 a - 4 b = -4 \\ a - b = -5\end{cases}\) \(\begin{vmatrix}1 \\ 4\end{vmatrix}\) geeft \(\begin{cases}3 a - 4 b = -4 \\ 4 a - 4 b = -20\end{cases}\)

Aftrekken geeft \(-a = 16 \text{,}\) dus \(a = -16 \text{.}\)

\(\begin{rcases}3 a - 4 b = -4 \\ a = -16\end{rcases} \begin{matrix}3 ⋅ -16 - 4 b = -4 \\ -4 b = 44 \\ b = -11\end{matrix}\)

De oplossing is \((a , b) = (-16 , -11) \text{.}\)

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

Aftrekken geeft \(2 p = 8 \text{,}\) dus \(p = 4 \text{.}\)

\(\begin{rcases}3 p + 5 q = -3 \\ p = 4\end{rcases} \begin{matrix}3 ⋅ 4 + 5 q = -3 \\ 5 q = -15 \\ q = -3\end{matrix}\)

De oplossing is \((p , q) = (4 , -3) \text{.}\)

Gelijk stellen geeft \(6 x - 13 = 8 x - 17\)

\(-2 x = -4\) dus \(x = 2\)

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

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

Substitutie geeft \(7 (8 y - 44) + 4 y = -8\)

Haakjes wegwerken geeft
\(56 y - 308 + 4 y = -8\)
\(60 y = 300\)
\(y = 5\)

\(\begin{rcases}x = 8 y - 44 \\ y = 5\end{rcases} \begin{matrix}x = 8 ⋅ 5 - 44 \\ x = -4\end{matrix}\)

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

Substitutie geeft \(x = 2 (5 x - 23) + 1\)

Haakjes wegwerken geeft
\(x = 10 x - 46 + 1\)
\(-9 x = -45\)
\(x = 5\)

\(\begin{rcases}y = 5 x - 23 \\ x = 5\end{rcases} \begin{matrix}y = 5 ⋅ 5 - 23 \\ y = 2\end{matrix}\)

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