Aftrekken geeft \(x = -2 \text{.}\)

\(\begin{rcases}4 x + 6 y = -5 \\ x = -2\end{rcases} \begin{matrix}4 ⋅ -2 + 6 y = -5 \\ 6 y = 3 \\ y = \frac{1}{2}\end{matrix}\)

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

\(\begin{cases}3 a - b = -5 \\ 2 a + 2 b = 6\end{cases}\) \(\begin{vmatrix}2 \\ 1\end{vmatrix}\) geeft \(\begin{cases}6 a - 2 b = -10 \\ 2 a + 2 b = 6\end{cases}\)

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

\(\begin{rcases}3 a - b = -5 \\ a = -\frac{1}{2}\end{rcases} \begin{matrix}3 ⋅ -\frac{1}{2} - b = -5 \\ -b = -3\frac{1}{2} \\ b = 3\frac{1}{2}\end{matrix}\)

De oplossing is \((a , b) = (-\frac{1}{2} , 3\frac{1}{2}) \text{.}\)

\(\begin{cases}6 a - 5 b = 2 \\ 5 a - 3 b = 4\end{cases}\) \(\begin{vmatrix}3 \\ 5\end{vmatrix}\) geeft \(\begin{cases}18 a - 15 b = 6 \\ 25 a - 15 b = 20\end{cases}\)

Aftrekken geeft \(-7 a = -14 \text{,}\) dus \(a = 2 \text{.}\)

\(\begin{rcases}6 a - 5 b = 2 \\ a = 2\end{rcases} \begin{matrix}6 ⋅ 2 - 5 b = 2 \\ -5 b = -10 \\ b = 2\end{matrix}\)

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

Gelijk stellen geeft \(9 x + 25 = 3 x + 7\)

\(6 x = -18\) dus \(x = -3\)

\(\begin{rcases}y = 9 x + 25 \\ x = -3\end{rcases} \begin{matrix}y = 9 ⋅ -3 + 25 \\ y = -2\end{matrix}\)

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

Substitutie geeft \(8 (2 q - 10) + 9 q = 20\)

Haakjes wegwerken geeft
\(16 q - 80 + 9 q = 20\)
\(25 q = 100\)
\(q = 4\)

\(\begin{rcases}p = 2 q - 10 \\ q = 4\end{rcases} \begin{matrix}p = 2 ⋅ 4 - 10 \\ p = -2\end{matrix}\)

De oplossing is \((p , q) = (-2 , 4) \text{.}\)

Substitutie geeft \(y = 6 (4 y + 4) + 22\)

Haakjes wegwerken geeft
\(y = 24 y + 24 + 22\)
\(-23 y = 46\)
\(y = -2\)

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

De oplossing is \((x , y) = (-4 , -2) \text{.}\)