Stelsels oplossen

Aftrekken geeft \(p = -8 \text{.}\)

\(\begin{rcases}4 p - q = -6 \\ p = -8\end{rcases} \begin{matrix}4 ⋅ -8 - q = -6 \\ -q = 26 \\ q = -26\end{matrix}\)

De oplossing is \((p , q) = (-8 , -26) \text{.}\)

\(\begin{cases}2 p + 6 q = -4 \\ p - q = 6\end{cases}\) \(\begin{vmatrix}1 \\ 6\end{vmatrix}\) geeft \(\begin{cases}2 p + 6 q = -4 \\ 6 p - 6 q = 36\end{cases}\)

Optellen geeft \(8 p = 32 \text{,}\) dus \(p = 4 \text{.}\)

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

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

\(\begin{cases}5 x - 6 y = -5 \\ 3 x - 4 y = -5\end{cases}\) \(\begin{vmatrix}2 \\ 3\end{vmatrix}\) geeft \(\begin{cases}10 x - 12 y = -10 \\ 9 x - 12 y = -15\end{cases}\)

Aftrekken geeft \(x = 5 \text{.}\)

\(\begin{rcases}5 x - 6 y = -5 \\ x = 5\end{rcases} \begin{matrix}5 ⋅ 5 - 6 y = -5 \\ -6 y = -30 \\ y = 5\end{matrix}\)

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

Gelijk stellen geeft \(9 x - 44 = 3 x - 14\)

\(6 x = 30\) dus \(x = 5\)

\(\begin{rcases}y = 9 x - 44 \\ x = 5\end{rcases} \begin{matrix}y = 9 ⋅ 5 - 44 \\ y = 1\end{matrix}\)

De oplossing is \((x , y) = (5 , 1) \text{.}\)

Substitutie geeft \(7 p + 5 (9 p + 22) = -46\)

Haakjes wegwerken geeft
\(7 p + 45 p + 110 = -46\)
\(52 p = -156\)
\(p = -3\)

\(\begin{rcases}q = 9 p + 22 \\ p = -3\end{rcases} \begin{matrix}q = 9 ⋅ -3 + 22 \\ q = -5\end{matrix}\)

De oplossing is \((p , q) = (-3 , -5) \text{.}\)

Substitutie geeft \(p = 7 (3 p + 6) + 38\)

Haakjes wegwerken geeft
\(p = 21 p + 42 + 38\)
\(-20 p = 80\)
\(p = -4\)

\(\begin{rcases}q = 3 p + 6 \\ p = -4\end{rcases} \begin{matrix}q = 3 ⋅ -4 + 6 \\ q = -6\end{matrix}\)

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