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

\(\begin{rcases}5 p - q = -2 \\ p = \frac{1}{2}\end{rcases} \begin{matrix}5 ⋅ \frac{1}{2} - q = -2 \\ -q = -4\frac{1}{2} \\ q = 4\frac{1}{2}\end{matrix}\)

De oplossing is \((p , q) = (\frac{1}{2} , 4\frac{1}{2}) \text{.}\)

\(\begin{cases}5 a + 3 b = -2 \\ 6 a + 6 b = 6\end{cases}\) \(\begin{vmatrix}2 \\ 1\end{vmatrix}\) geeft \(\begin{cases}10 a + 6 b = -4 \\ 6 a + 6 b = 6\end{cases}\)

Aftrekken geeft \(4 a = -10 \text{,}\) dus \(a = -2\frac{1}{2} \text{.}\)

\(\begin{rcases}5 a + 3 b = -2 \\ a = -2\frac{1}{2}\end{rcases} \begin{matrix}5 ⋅ -2\frac{1}{2} + 3 b = -2 \\ 3 b = 10\frac{1}{2} \\ b = 3\frac{1}{2}\end{matrix}\)

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

\(\begin{cases}5 x - 4 y = -6 \\ 6 x - 6 y = -3\end{cases}\) \(\begin{vmatrix}3 \\ 2\end{vmatrix}\) geeft \(\begin{cases}15 x - 12 y = -18 \\ 12 x - 12 y = -6\end{cases}\)

Aftrekken geeft \(3 x = -12 \text{,}\) dus \(x = -4 \text{.}\)

\(\begin{rcases}5 x - 4 y = -6 \\ x = -4\end{rcases} \begin{matrix}5 ⋅ -4 - 4 y = -6 \\ -4 y = 14 \\ y = -3\frac{1}{2}\end{matrix}\)

De oplossing is \((x , y) = (-4 , -3\frac{1}{2}) \text{.}\)

Gelijk stellen geeft \(3 x + 13 = 5 x + 19\)

\(-2 x = 6\) dus \(x = -3\)

\(\begin{rcases}y = 3 x + 13 \\ x = -3\end{rcases} \begin{matrix}y = 3 ⋅ -3 + 13 \\ y = 4\end{matrix}\)

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

Substitutie geeft \(2 a + 3 (5 a - 24) = -4\)

Haakjes wegwerken geeft
\(2 a + 15 a - 72 = -4\)
\(17 a = 68\)
\(a = 4\)

\(\begin{rcases}b = 5 a - 24 \\ a = 4\end{rcases} \begin{matrix}b = 5 ⋅ 4 - 24 \\ b = -4\end{matrix}\)

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

Substitutie geeft \(x = 8 (4 x - 29) + 46\)

Haakjes wegwerken geeft
\(x = 32 x - 232 + 46\)
\(-31 x = -186\)
\(x = 6\)

\(\begin{rcases}y = 4 x - 29 \\ x = 6\end{rcases} \begin{matrix}y = 4 ⋅ 6 - 29 \\ y = -5\end{matrix}\)

De oplossing is \((x , y) = (6 , -5) \text{.}\)