Optellen geeft \(3 a = -9 \text{,}\) dus \(a = -3 \text{.}\)

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

De oplossing is \((a , b) = (-3 , 3) \text{.}\)

\(\begin{cases}2 x - 3 y = -5 \\ 3 x - 6 y = 3\end{cases}\) \(\begin{vmatrix}2 \\ 1\end{vmatrix}\) geeft \(\begin{cases}4 x - 6 y = -10 \\ 3 x - 6 y = 3\end{cases}\)

Aftrekken geeft \(x = -13 \text{.}\)

\(\begin{rcases}2 x - 3 y = -5 \\ x = -13\end{rcases} \begin{matrix}2 ⋅ -13 - 3 y = -5 \\ -3 y = 21 \\ y = -7\end{matrix}\)

De oplossing is \((x , y) = (-13 , -7) \text{.}\)

\(\begin{cases}2 p + 3 q = -6 \\ 5 p + 5 q = -5\end{cases}\) \(\begin{vmatrix}5 \\ 3\end{vmatrix}\) geeft \(\begin{cases}10 p + 15 q = -30 \\ 15 p + 15 q = -15\end{cases}\)

Aftrekken geeft \(-5 p = -15 \text{,}\) dus \(p = 3 \text{.}\)

\(\begin{rcases}2 p + 3 q = -6 \\ p = 3\end{rcases} \begin{matrix}2 ⋅ 3 + 3 q = -6 \\ 3 q = -12 \\ q = -4\end{matrix}\)

De oplossing is \((p , q) = (3 , -4) \text{.}\)

Gelijk stellen geeft \(5 x + 7 = 3 x + 3\)

\(2 x = -4\) dus \(x = -2\)

\(\begin{rcases}y = 5 x + 7 \\ x = -2\end{rcases} \begin{matrix}y = 5 ⋅ -2 + 7 \\ y = -3\end{matrix}\)

De oplossing is \((x , y) = (-2 , -3) \text{.}\)

Substitutie geeft \(5 x + 9 (7 x - 30) = 2\)

Haakjes wegwerken geeft
\(5 x + 63 x - 270 = 2\)
\(68 x = 272\)
\(x = 4\)

\(\begin{rcases}y = 7 x - 30 \\ x = 4\end{rcases} \begin{matrix}y = 7 ⋅ 4 - 30 \\ y = -2\end{matrix}\)

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

Substitutie geeft \(a = 5 (7 a - 30) + 14\)

Haakjes wegwerken geeft
\(a = 35 a - 150 + 14\)
\(-34 a = -136\)
\(a = 4\)

\(\begin{rcases}b = 7 a - 30 \\ a = 4\end{rcases} \begin{matrix}b = 7 ⋅ 4 - 30 \\ b = -2\end{matrix}\)

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