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

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

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

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

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

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

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

\(\begin{cases}2 a - 5 b = 6 \\ 3 a - 6 b = 3\end{cases}\) \(\begin{vmatrix}6 \\ 5\end{vmatrix}\) geeft \(\begin{cases}12 a - 30 b = 36 \\ 15 a - 30 b = 15\end{cases}\)

Aftrekken geeft \(-3 a = 21 \text{,}\) dus \(a = -7 \text{.}\)

\(\begin{rcases}2 a - 5 b = 6 \\ a = -7\end{rcases} \begin{matrix}2 ⋅ -7 - 5 b = 6 \\ -5 b = 20 \\ b = -4\end{matrix}\)

De oplossing is \((a , b) = (-7 , -4) \text{.}\)

Gelijk stellen geeft \(2 x + 12 = 4 x + 22\)

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

\(\begin{rcases}y = 2 x + 12 \\ x = -5\end{rcases} \begin{matrix}y = 2 ⋅ -5 + 12 \\ y = 2\end{matrix}\)

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

Substitutie geeft \(8 x + 5 (4 x + 23) = -53\)

Haakjes wegwerken geeft
\(8 x + 20 x + 115 = -53\)
\(28 x = -168\)
\(x = -6\)

\(\begin{rcases}y = 4 x + 23 \\ x = -6\end{rcases} \begin{matrix}y = 4 ⋅ -6 + 23 \\ y = -1\end{matrix}\)

De oplossing is \((x , y) = (-6 , -1) \text{.}\)

Substitutie geeft \(b = 2 (6 b + 42) - 18\)

Haakjes wegwerken geeft
\(b = 12 b + 84 - 18\)
\(-11 b = 66\)
\(b = -6\)

\(\begin{rcases}a = 6 b + 42 \\ b = -6\end{rcases} \begin{matrix}a = 6 ⋅ -6 + 42 \\ a = 6\end{matrix}\)

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