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

\(\begin{rcases}4 a - 4 b = 2 \\ b = 4\end{rcases} \begin{matrix}4 a - 4 ⋅ 4 = 2 \\ 4 a = 18 \\ a = 4\frac{1}{2}\end{matrix}\)

De oplossing is \((a , b) = (4\frac{1}{2} , 4) \text{.}\)

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

Aftrekken geeft \(2 a = 4 \text{,}\) dus \(a = 2 \text{.}\)

\(\begin{rcases}4 a - 2 b = -1 \\ a = 2\end{rcases} \begin{matrix}4 ⋅ 2 - 2 b = -1 \\ -2 b = -9 \\ b = 4\frac{1}{2}\end{matrix}\)

De oplossing is \((a , b) = (2 , 4\frac{1}{2}) \text{.}\)

\(\begin{cases}3 x - 3 y = 3 \\ 2 x + 4 y = 5\end{cases}\) \(\begin{vmatrix}4 \\ 3\end{vmatrix}\) geeft \(\begin{cases}12 x - 12 y = 12 \\ 6 x + 12 y = 15\end{cases}\)

Optellen geeft \(18 x = 27 \text{,}\) dus \(x = 1\frac{1}{2} \text{.}\)

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

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

Gelijk stellen geeft \(6 x + 32 = 4 x + 22\)

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

\(\begin{rcases}y = 6 x + 32 \\ x = -5\end{rcases} \begin{matrix}y = 6 ⋅ -5 + 32 \\ y = 2\end{matrix}\)

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

Substitutie geeft \(9 (7 y + 17) + 3 y = -45\)

Haakjes wegwerken geeft
\(63 y + 153 + 3 y = -45\)
\(66 y = -198\)
\(y = -3\)

\(\begin{rcases}x = 7 y + 17 \\ y = -3\end{rcases} \begin{matrix}x = 7 ⋅ -3 + 17 \\ x = -4\end{matrix}\)

De oplossing is \((x , y) = (-4 , -3) \text{.}\)

Substitutie geeft \(p = 6 (9 p + 37) - 10\)

Haakjes wegwerken geeft
\(p = 54 p + 222 - 10\)
\(-53 p = 212\)
\(p = -4\)

\(\begin{rcases}q = 9 p + 37 \\ p = -4\end{rcases} \begin{matrix}q = 9 ⋅ -4 + 37 \\ q = 1\end{matrix}\)

De oplossing is \((p , q) = (-4 , 1) \text{.}\)