Aftrekken geeft \(a = -6 \text{.}\)

\(\begin{rcases}4 a - 3 b = -3 \\ a = -6\end{rcases} \begin{matrix}4 ⋅ -6 - 3 b = -3 \\ -3 b = 21 \\ b = -7\end{matrix}\)

De oplossing is \((a , b) = (-6 , -7) \text{.}\)

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

Aftrekken geeft \(x = -4 \text{.}\)

\(\begin{rcases}4 x + 3 y = 2 \\ x = -4\end{rcases} \begin{matrix}4 ⋅ -4 + 3 y = 2 \\ 3 y = 18 \\ y = 6\end{matrix}\)

De oplossing is \((x , y) = (-4 , 6) \text{.}\)

\(\begin{cases}2 p + 2 q = 4 \\ 3 p - 3 q = 3\end{cases}\) \(\begin{vmatrix}3 \\ 2\end{vmatrix}\) geeft \(\begin{cases}6 p + 6 q = 12 \\ 6 p - 6 q = 6\end{cases}\)

Optellen geeft \(12 p = 18 \text{,}\) dus \(p = 1\frac{1}{2} \text{.}\)

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

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

Gelijk stellen geeft \(4 x + 13 = 9 x + 28\)

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

\(\begin{rcases}y = 4 x + 13 \\ x = -3\end{rcases} \begin{matrix}y = 4 ⋅ -3 + 13 \\ y = 1\end{matrix}\)

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

Substitutie geeft \(5 (8 y + 34) + 2 y = -40\)

Haakjes wegwerken geeft
\(40 y + 170 + 2 y = -40\)
\(42 y = -210\)
\(y = -5\)

\(\begin{rcases}x = 8 y + 34 \\ y = -5\end{rcases} \begin{matrix}x = 8 ⋅ -5 + 34 \\ x = -6\end{matrix}\)

De oplossing is \((x , y) = (-6 , -5) \text{.}\)

Substitutie geeft \(a = 3 (7 a - 34) + 2\)

Haakjes wegwerken geeft
\(a = 21 a - 102 + 2\)
\(-20 a = -100\)
\(a = 5\)

\(\begin{rcases}b = 7 a - 34 \\ a = 5\end{rcases} \begin{matrix}b = 7 ⋅ 5 - 34 \\ b = 1\end{matrix}\)

De oplossing is \((a , b) = (5 , 1) \text{.}\)