Optellen geeft \(4 a = -2 \text{,}\) dus \(a = -\frac{1}{2} \text{.}\)

\(\begin{rcases}3 a - b = 2 \\ a = -\frac{1}{2}\end{rcases} \begin{matrix}3 ⋅ -\frac{1}{2} - b = 2 \\ -b = 3\frac{1}{2} \\ b = -3\frac{1}{2}\end{matrix}\)

De oplossing is \((a , b) = (-\frac{1}{2} , -3\frac{1}{2}) \text{.}\)

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

Aftrekken geeft \(2 x = -8 \text{,}\) dus \(x = -4 \text{.}\)

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

De oplossing is \((x , y) = (-4 , -3) \text{.}\)

\(\begin{cases}4 a + 5 b = -2 \\ 5 a + 6 b = -4\end{cases}\) \(\begin{vmatrix}6 \\ 5\end{vmatrix}\) geeft \(\begin{cases}24 a + 30 b = -12 \\ 25 a + 30 b = -20\end{cases}\)

Aftrekken geeft \(-a = 8 \text{,}\) dus \(a = -8 \text{.}\)

\(\begin{rcases}4 a + 5 b = -2 \\ a = -8\end{rcases} \begin{matrix}4 ⋅ -8 + 5 b = -2 \\ 5 b = 30 \\ b = 6\end{matrix}\)

De oplossing is \((a , b) = (-8 , 6) \text{.}\)

Gelijk stellen geeft \(2 x - 4 = 8 x - 10\)

\(-6 x = -6\) dus \(x = 1\)

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

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

Substitutie geeft \(4 (7 y + 43) + 9 y = -50\)

Haakjes wegwerken geeft
\(28 y + 172 + 9 y = -50\)
\(37 y = -222\)
\(y = -6\)

\(\begin{rcases}x = 7 y + 43 \\ y = -6\end{rcases} \begin{matrix}x = 7 ⋅ -6 + 43 \\ x = 1\end{matrix}\)

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

Substitutie geeft \(q = 4 (7 q - 25) - 8\)

Haakjes wegwerken geeft
\(q = 28 q - 100 - 8\)
\(-27 q = -108\)
\(q = 4\)

\(\begin{rcases}p = 7 q - 25 \\ q = 4\end{rcases} \begin{matrix}p = 7 ⋅ 4 - 25 \\ p = 3\end{matrix}\)

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