Aftrekken geeft \(-2 y = 6 \text{,}\) dus \(y = -3 \text{.}\)

\(\begin{rcases}x + y = 4 \\ y = -3\end{rcases} \begin{matrix}x - 3 = 4 \\ x = 7\end{matrix}\)

De oplossing is \((x , y) = (7 , -3) \text{.}\)

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

Optellen geeft \(10 a = -5 \text{,}\) dus \(a = -\frac{1}{2} \text{.}\)

\(\begin{rcases}4 a - 2 b = -1 \\ a = -\frac{1}{2}\end{rcases} \begin{matrix}4 ⋅ -\frac{1}{2} - 2 b = -1 \\ -2 b = 1 \\ b = -\frac{1}{2}\end{matrix}\)

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

\(\begin{cases}3 x - 5 y = 3 \\ 4 x - 6 y = -2\end{cases}\) \(\begin{vmatrix}6 \\ 5\end{vmatrix}\) geeft \(\begin{cases}18 x - 30 y = 18 \\ 20 x - 30 y = -10\end{cases}\)

Aftrekken geeft \(-2 x = 28 \text{,}\) dus \(x = -14 \text{.}\)

\(\begin{rcases}3 x - 5 y = 3 \\ x = -14\end{rcases} \begin{matrix}3 ⋅ -14 - 5 y = 3 \\ -5 y = 45 \\ y = -9\end{matrix}\)

De oplossing is \((x , y) = (-14 , -9) \text{.}\)

Gelijk stellen geeft \(3 x - 13 = 9 x - 37\)

\(-6 x = -24\) dus \(x = 4\)

\(\begin{rcases}y = 3 x - 13 \\ x = 4\end{rcases} \begin{matrix}y = 3 ⋅ 4 - 13 \\ y = -1\end{matrix}\)

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

Substitutie geeft \(9 p + 8 (4 p + 18) = -20\)

Haakjes wegwerken geeft
\(9 p + 32 p + 144 = -20\)
\(41 p = -164\)
\(p = -4\)

\(\begin{rcases}q = 4 p + 18 \\ p = -4\end{rcases} \begin{matrix}q = 4 ⋅ -4 + 18 \\ q = 2\end{matrix}\)

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

Substitutie geeft \(b = 8 (2 b - 11) + 43\)

Haakjes wegwerken geeft
\(b = 16 b - 88 + 43\)
\(-15 b = -45\)
\(b = 3\)

\(\begin{rcases}a = 2 b - 11 \\ b = 3\end{rcases} \begin{matrix}a = 2 ⋅ 3 - 11 \\ a = -5\end{matrix}\)

De oplossing is \((a , b) = (-5 , 3) \text{.}\)