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

\(\begin{rcases}4 p - q = 4 \\ p = -\frac{1}{2}\end{rcases} \begin{matrix}4 ⋅ -\frac{1}{2} - q = 4 \\ -q = 6 \\ q = -6\end{matrix}\)

De oplossing is \((p , q) = (-\frac{1}{2} , -6) \text{.}\)

\(\begin{cases}2 a - b = -6 \\ a + 4 b = 6\end{cases}\) \(\begin{vmatrix}4 \\ 1\end{vmatrix}\) geeft \(\begin{cases}8 a - 4 b = -24 \\ a + 4 b = 6\end{cases}\)

Optellen geeft \(9 a = -18 \text{,}\) dus \(a = -2 \text{.}\)

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

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

\(\begin{cases}2 x + 2 y = -4 \\ 3 x + 5 y = 5\end{cases}\) \(\begin{vmatrix}5 \\ 2\end{vmatrix}\) geeft \(\begin{cases}10 x + 10 y = -20 \\ 6 x + 10 y = 10\end{cases}\)

Aftrekken geeft \(4 x = -30 \text{,}\) dus \(x = -7\frac{1}{2} \text{.}\)

\(\begin{rcases}2 x + 2 y = -4 \\ x = -7\frac{1}{2}\end{rcases} \begin{matrix}2 ⋅ -7\frac{1}{2} + 2 y = -4 \\ 2 y = 11 \\ y = 5\frac{1}{2}\end{matrix}\)

De oplossing is \((x , y) = (-7\frac{1}{2} , 5\frac{1}{2}) \text{.}\)

Gelijk stellen geeft \(4 x - 7 = 6 x - 11\)

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

\(\begin{rcases}y = 4 x - 7 \\ x = 2\end{rcases} \begin{matrix}y = 4 ⋅ 2 - 7 \\ y = 1\end{matrix}\)

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

Substitutie geeft \(7 (8 b - 18) + 6 b = 60\)

Haakjes wegwerken geeft
\(56 b - 126 + 6 b = 60\)
\(62 b = 186\)
\(b = 3\)

\(\begin{rcases}a = 8 b - 18 \\ b = 3\end{rcases} \begin{matrix}a = 8 ⋅ 3 - 18 \\ a = 6\end{matrix}\)

De oplossing is \((a , b) = (6 , 3) \text{.}\)

Substitutie geeft \(x = 6 (3 x - 15) + 39\)

Haakjes wegwerken geeft
\(x = 18 x - 90 + 39\)
\(-17 x = -51\)
\(x = 3\)

\(\begin{rcases}y = 3 x - 15 \\ x = 3\end{rcases} \begin{matrix}y = 3 ⋅ 3 - 15 \\ y = -6\end{matrix}\)

De oplossing is \((x , y) = (3 , -6) \text{.}\)