Aftrekken geeft \(-4 x = -2 \text{,}\) dus \(x = \frac{1}{2} \text{.}\)

\(\begin{rcases}2 x + y = -3 \\ x = \frac{1}{2}\end{rcases} \begin{matrix}2 ⋅ \frac{1}{2} + y = -3 \\ y = -4\end{matrix}\)

De oplossing is \((x , y) = (\frac{1}{2} , -4) \text{.}\)

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

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

\(\begin{rcases}2 a - 2 b = -3 \\ a = 2\end{rcases} \begin{matrix}2 ⋅ 2 - 2 b = -3 \\ -2 b = -7 \\ b = 3\frac{1}{2}\end{matrix}\)

De oplossing is \((a , b) = (2 , 3\frac{1}{2}) \text{.}\)

\(\begin{cases}2 x + 2 y = -2 \\ 5 x - 3 y = -1\end{cases}\) \(\begin{vmatrix}3 \\ 2\end{vmatrix}\) geeft \(\begin{cases}6 x + 6 y = -6 \\ 10 x - 6 y = -2\end{cases}\)

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

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

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

Gelijk stellen geeft \(7 x + 10 = 3 x + 6\)

\(4 x = -4\) dus \(x = -1\)

\(\begin{rcases}y = 7 x + 10 \\ x = -1\end{rcases} \begin{matrix}y = 7 ⋅ -1 + 10 \\ y = 3\end{matrix}\)

De oplossing is \((x , y) = (-1 , 3) \text{.}\)

Substitutie geeft \(5 (4 b - 4) + 6 b = 32\)

Haakjes wegwerken geeft
\(20 b - 20 + 6 b = 32\)
\(26 b = 52\)
\(b = 2\)

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

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

Substitutie geeft \(p = 4 (9 p - 13) + 17\)

Haakjes wegwerken geeft
\(p = 36 p - 52 + 17\)
\(-35 p = -35\)
\(p = 1\)

\(\begin{rcases}q = 9 p - 13 \\ p = 1\end{rcases} \begin{matrix}q = 9 ⋅ 1 - 13 \\ q = -4\end{matrix}\)

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