Aftrekken geeft \(8 b = -12 \text{,}\) dus \(b = -1\frac{1}{2} \text{.}\)

\(\begin{rcases}a + 3 b = -6 \\ b = -1\frac{1}{2}\end{rcases} \begin{matrix}a + 3 ⋅ -1\frac{1}{2} = -6 \\ a = -1\frac{1}{2}\end{matrix}\)

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

\(\begin{cases}2 x - 3 y = 2 \\ x - y = -1\end{cases}\) \(\begin{vmatrix}1 \\ 3\end{vmatrix}\) geeft \(\begin{cases}2 x - 3 y = 2 \\ 3 x - 3 y = -3\end{cases}\)

Aftrekken geeft \(-x = 5 \text{,}\) dus \(x = -5 \text{.}\)

\(\begin{rcases}2 x - 3 y = 2 \\ x = -5\end{rcases} \begin{matrix}2 ⋅ -5 - 3 y = 2 \\ -3 y = 12 \\ y = -4\end{matrix}\)

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

\(\begin{cases}5 a + 5 b = -5 \\ 3 a - 3 b = -6\end{cases}\) \(\begin{vmatrix}3 \\ 5\end{vmatrix}\) geeft \(\begin{cases}15 a + 15 b = -15 \\ 15 a - 15 b = -30\end{cases}\)

Optellen geeft \(30 a = -45 \text{,}\) dus \(a = -1\frac{1}{2} \text{.}\)

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

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

Gelijk stellen geeft \(3 x + 5 = 7 x + 17\)

\(-4 x = 12\) dus \(x = -3\)

\(\begin{rcases}y = 3 x + 5 \\ x = -3\end{rcases} \begin{matrix}y = 3 ⋅ -3 + 5 \\ y = -4\end{matrix}\)

De oplossing is \((x , y) = (-3 , -4) \text{.}\)

Substitutie geeft \(6 x + 9 (2 x + 4) = -36\)

Haakjes wegwerken geeft
\(6 x + 18 x + 36 = -36\)
\(24 x = -72\)
\(x = -3\)

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

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

Substitutie geeft \(q = 5 (9 q + 52) + 4\)

Haakjes wegwerken geeft
\(q = 45 q + 260 + 4\)
\(-44 q = 264\)
\(q = -6\)

\(\begin{rcases}p = 9 q + 52 \\ q = -6\end{rcases} \begin{matrix}p = 9 ⋅ -6 + 52 \\ p = -2\end{matrix}\)

De oplossing is \((p , q) = (-2 , -6) \text{.}\)