Aftrekken geeft \(-y = 9 \text{,}\) dus \(y = -9 \text{.}\)

\(\begin{rcases}3 x - 4 y = 3 \\ y = -9\end{rcases} \begin{matrix}3 x - 4 ⋅ -9 = 3 \\ 3 x = -33 \\ x = -11\end{matrix}\)

De oplossing is \((x , y) = (-11 , -9) \text{.}\)

\(\begin{cases}4 x + 2 y = -6 \\ 6 x - y = -1\end{cases}\) \(\begin{vmatrix}1 \\ 2\end{vmatrix}\) geeft \(\begin{cases}4 x + 2 y = -6 \\ 12 x - 2 y = -2\end{cases}\)

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

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

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

\(\begin{cases}2 p - 2 q = 4 \\ 5 p - 3 q = -2\end{cases}\) \(\begin{vmatrix}3 \\ 2\end{vmatrix}\) geeft \(\begin{cases}6 p - 6 q = 12 \\ 10 p - 6 q = -4\end{cases}\)

Aftrekken geeft \(-4 p = 16 \text{,}\) dus \(p = -4 \text{.}\)

\(\begin{rcases}2 p - 2 q = 4 \\ p = -4\end{rcases} \begin{matrix}2 ⋅ -4 - 2 q = 4 \\ -2 q = 12 \\ q = -6\end{matrix}\)

De oplossing is \((p , q) = (-4 , -6) \text{.}\)

Gelijk stellen geeft \(7 x + 16 = 5 x + 12\)

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

\(\begin{rcases}y = 7 x + 16 \\ x = -2\end{rcases} \begin{matrix}y = 7 ⋅ -2 + 16 \\ y = 2\end{matrix}\)

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

Substitutie geeft \(4 (6 b - 6) + 2 b = 28\)

Haakjes wegwerken geeft
\(24 b - 24 + 2 b = 28\)
\(26 b = 52\)
\(b = 2\)

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

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

Substitutie geeft \(a = 2 (6 a + 3) + 5\)

Haakjes wegwerken geeft
\(a = 12 a + 6 + 5\)
\(-11 a = 11\)
\(a = -1\)

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

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