Aftrekken geeft \(-y = 12 \text{,}\) dus \(y = -12 \text{.}\)

\(\begin{rcases}3 x + y = 6 \\ y = -12\end{rcases} \begin{matrix}3 x - 12 = 6 \\ 3 x = 18 \\ x = 6\end{matrix}\)

De oplossing is \((x , y) = (6 , -12) \text{.}\)

\(\begin{cases}2 p - 2 q = 3 \\ 5 p - 4 q = -2\end{cases}\) \(\begin{vmatrix}2 \\ 1\end{vmatrix}\) geeft \(\begin{cases}4 p - 4 q = 6 \\ 5 p - 4 q = -2\end{cases}\)

Aftrekken geeft \(-p = 8 \text{,}\) dus \(p = -8 \text{.}\)

\(\begin{rcases}2 p - 2 q = 3 \\ p = -8\end{rcases} \begin{matrix}2 ⋅ -8 - 2 q = 3 \\ -2 q = 19 \\ q = -9\frac{1}{2}\end{matrix}\)

De oplossing is \((p , q) = (-8 , -9\frac{1}{2}) \text{.}\)

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

Optellen geeft \(16 x = 8 \text{,}\) dus \(x = \frac{1}{2} \text{.}\)

\(\begin{rcases}5 x + 3 y = -5 \\ x = \frac{1}{2}\end{rcases} \begin{matrix}5 ⋅ \frac{1}{2} + 3 y = -5 \\ 3 y = -7\frac{1}{2} \\ y = -2\frac{1}{2}\end{matrix}\)

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

Gelijk stellen geeft \(8 x - 37 = 5 x - 25\)

\(3 x = 12\) dus \(x = 4\)

\(\begin{rcases}y = 8 x - 37 \\ x = 4\end{rcases} \begin{matrix}y = 8 ⋅ 4 - 37 \\ y = -5\end{matrix}\)

De oplossing is \((x , y) = (4 , -5) \text{.}\)

Substitutie geeft \(6 a + 2 (3 a + 6) = 0\)

Haakjes wegwerken geeft
\(6 a + 6 a + 12 = 0\)
\(12 a = -12\)
\(a = -1\)

\(\begin{rcases}b = 3 a + 6 \\ a = -1\end{rcases} \begin{matrix}b = 3 ⋅ -1 + 6 \\ b = 3\end{matrix}\)

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

Substitutie geeft \(a = 6 (8 a + 25) - 9\)

Haakjes wegwerken geeft
\(a = 48 a + 150 - 9\)
\(-47 a = 141\)
\(a = -3\)

\(\begin{rcases}b = 8 a + 25 \\ a = -3\end{rcases} \begin{matrix}b = 8 ⋅ -3 + 25 \\ b = 1\end{matrix}\)

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