Aftrekken geeft \(-b = -6 \text{,}\) dus \(b = 6 \text{.}\)

\(\begin{rcases}4 a + 3 b = -2 \\ b = 6\end{rcases} \begin{matrix}4 a + 3 ⋅ 6 = -2 \\ 4 a = -20 \\ a = -5\end{matrix}\)

De oplossing is \((a , b) = (-5 , 6) \text{.}\)

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

Optellen geeft \(10 a = -15 \text{,}\) dus \(a = -1\frac{1}{2} \text{.}\)

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

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

\(\begin{cases}6 x - 4 y = -6 \\ 5 x - 6 y = 3\end{cases}\) \(\begin{vmatrix}3 \\ 2\end{vmatrix}\) geeft \(\begin{cases}18 x - 12 y = -18 \\ 10 x - 12 y = 6\end{cases}\)

Aftrekken geeft \(8 x = -24 \text{,}\) dus \(x = -3 \text{.}\)

\(\begin{rcases}6 x - 4 y = -6 \\ x = -3\end{rcases} \begin{matrix}6 ⋅ -3 - 4 y = -6 \\ -4 y = 12 \\ y = -3\end{matrix}\)

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

Gelijk stellen geeft \(9 x + 42 = 7 x + 32\)

\(2 x = -10\) dus \(x = -5\)

\(\begin{rcases}y = 9 x + 42 \\ x = -5\end{rcases} \begin{matrix}y = 9 ⋅ -5 + 42 \\ y = -3\end{matrix}\)

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

Substitutie geeft \(6 (9 y - 51) + 3 y = -21\)

Haakjes wegwerken geeft
\(54 y - 306 + 3 y = -21\)
\(57 y = 285\)
\(y = 5\)

\(\begin{rcases}x = 9 y - 51 \\ y = 5\end{rcases} \begin{matrix}x = 9 ⋅ 5 - 51 \\ x = -6\end{matrix}\)

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

Substitutie geeft \(q = 8 (6 q - 11) - 6\)

Haakjes wegwerken geeft
\(q = 48 q - 88 - 6\)
\(-47 q = -94\)
\(q = 2\)

\(\begin{rcases}p = 6 q - 11 \\ q = 2\end{rcases} \begin{matrix}p = 6 ⋅ 2 - 11 \\ p = 1\end{matrix}\)

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