Aftrekken geeft \(x = -7 \text{.}\)

\(\begin{rcases}5 x - 2 y = -4 \\ x = -7\end{rcases} \begin{matrix}5 ⋅ -7 - 2 y = -4 \\ -2 y = 31 \\ y = -15\frac{1}{2}\end{matrix}\)

De oplossing is \((x , y) = (-7 , -15\frac{1}{2}) \text{.}\)

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

Aftrekken geeft \(y = -10 \text{.}\)

\(\begin{rcases}4 x - 3 y = -4 \\ y = -10\end{rcases} \begin{matrix}4 x - 3 ⋅ -10 = -4 \\ 4 x = -34 \\ x = -8\frac{1}{2}\end{matrix}\)

De oplossing is \((x , y) = (-8\frac{1}{2} , -10) \text{.}\)

\(\begin{cases}2 a + 4 b = -1 \\ 3 a - 3 b = 3\end{cases}\) \(\begin{vmatrix}3 \\ 4\end{vmatrix}\) geeft \(\begin{cases}6 a + 12 b = -3 \\ 12 a - 12 b = 12\end{cases}\)

Optellen geeft \(18 a = 9 \text{,}\) dus \(a = \frac{1}{2} \text{.}\)

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

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

Gelijk stellen geeft \(8 y + 45 = 5 y + 30\)

\(3 y = -15\) dus \(y = -5\)

\(\begin{rcases}x = 8 y + 45 \\ y = -5\end{rcases} \begin{matrix}x = 8 ⋅ -5 + 45 \\ x = 5\end{matrix}\)

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

Substitutie geeft \(6 a + 8 (4 a - 2) = -54\)

Haakjes wegwerken geeft
\(6 a + 32 a - 16 = -54\)
\(38 a = -38\)
\(a = -1\)

\(\begin{rcases}b = 4 a - 2 \\ a = -1\end{rcases} \begin{matrix}b = 4 ⋅ -1 - 2 \\ b = -6\end{matrix}\)

De oplossing is \((a , b) = (-1 , -6) \text{.}\)

Substitutie geeft \(p = 7 (2 p + 12) - 32\)

Haakjes wegwerken geeft
\(p = 14 p + 84 - 32\)
\(-13 p = 52\)
\(p = -4\)

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

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