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

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

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

\(\begin{cases}4 a - 6 b = -2 \\ 2 a - 2 b = -5\end{cases}\) \(\begin{vmatrix}1 \\ 3\end{vmatrix}\) geeft \(\begin{cases}4 a - 6 b = -2 \\ 6 a - 6 b = -15\end{cases}\)

Aftrekken geeft \(-2 a = 13 \text{,}\) dus \(a = -6\frac{1}{2} \text{.}\)

\(\begin{rcases}4 a - 6 b = -2 \\ a = -6\frac{1}{2}\end{rcases} \begin{matrix}4 ⋅ -6\frac{1}{2} - 6 b = -2 \\ -6 b = 24 \\ b = -4\end{matrix}\)

De oplossing is \((a , b) = (-6\frac{1}{2} , -4) \text{.}\)

\(\begin{cases}5 a + 6 b = 5 \\ 3 a + 4 b = 2\end{cases}\) \(\begin{vmatrix}2 \\ 3\end{vmatrix}\) geeft \(\begin{cases}10 a + 12 b = 10 \\ 9 a + 12 b = 6\end{cases}\)

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

\(\begin{rcases}5 a + 6 b = 5 \\ a = 4\end{rcases} \begin{matrix}5 ⋅ 4 + 6 b = 5 \\ 6 b = -15 \\ b = -2\frac{1}{2}\end{matrix}\)

De oplossing is \((a , b) = (4 , -2\frac{1}{2}) \text{.}\)

Gelijk stellen geeft \(6 x + 13 = 3 x + 4\)

\(3 x = -9\) dus \(x = -3\)

\(\begin{rcases}y = 6 x + 13 \\ x = -3\end{rcases} \begin{matrix}y = 6 ⋅ -3 + 13 \\ y = -5\end{matrix}\)

De oplossing is \((x , y) = (-3 , -5) \text{.}\)

Substitutie geeft \(3 (5 y - 26) + 8 y = 14\)

Haakjes wegwerken geeft
\(15 y - 78 + 8 y = 14\)
\(23 y = 92\)
\(y = 4\)

\(\begin{rcases}x = 5 y - 26 \\ y = 4\end{rcases} \begin{matrix}x = 5 ⋅ 4 - 26 \\ x = -6\end{matrix}\)

De oplossing is \((x , y) = (-6 , 4) \text{.}\)

Substitutie geeft \(q = 7 (4 q - 2) - 13\)

Haakjes wegwerken geeft
\(q = 28 q - 14 - 13\)
\(-27 q = -27\)
\(q = 1\)

\(\begin{rcases}p = 4 q - 2 \\ q = 1\end{rcases} \begin{matrix}p = 4 ⋅ 1 - 2 \\ p = 2\end{matrix}\)

De oplossing is \((p , q) = (2 , 1) \text{.}\)