\(k \parallel l \text{,}\) dus \(l{:}\,x - 2 y = c \text{.}\)

\(\begin{rcases}x - 2 y = c \\ \text{door } A (7 , 4)\end{rcases} c = 1 ⋅ 7 - 2 ⋅ 4 = -1\)
Dus \(l{:}\,x - 2 y = -1 \text{.}\)

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

Optellen geeft \(5 x = -5\) dus \(x = -1 \text{.}\)

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

Dus \(S (-1 , -\frac{1}{2}) \text{.}\)

Substitutie geeft \(4 x + 1 (-2 x - 2) = -5\)

\(4 x - 2 x - 2 = -5\)
\(2 x = -3\)
Dus \(x = -1\frac{1}{2} \text{.}\)

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

Dus \(S (-1\frac{1}{2} , 1) \text{.}\)

\(k{:}\,x + 7 y = -4\) omschrijven geeft \(y = -\frac{1}{7} x - \frac{4}{7}\) dus \(\text{rc}_{k} = -\frac{1}{7} \text{.}\)
\(l{:}\,5 x - 3 y = -6\) omschrijven geeft \(y = 1\frac{2}{3} x + 2\) dus \(\text{rc}_{l} = 1\frac{2}{3} \text{.}\)

\(\tan(\alpha ) = -\frac{1}{7}\) geeft \(\alpha = \tan^{-1}(-\frac{1}{7}) = -8{,}13...\degree \text{.}\)
\(\tan(\beta ) = 1\frac{2}{3}\) geeft \(\beta = \tan^{-1}(1\frac{2}{3}) = 59{,}03...\degree \text{.}\)

\(\varphi = \alpha - \beta = -8{,}13...\degree - 59{,}03...\degree = -67{,}16...\degree \text{,}\) dus de gevraagde hoek is \(67{,}2\degree \text{.}\)

\(\frac{6}{12} = \frac{1}{2} = \frac{3}{6} \text{,}\) dus de lijnen \(k\) en \(l\) vallen samen.

\({p \over \frac{5}{2}} = {-4 \over -2} = {q \over -\frac{3}{2}}\)

\({p \over \frac{5}{2}} = {-4 \over -2}\) geeft \(p = 5\) en \({-4 \over -2} = {q \over -\frac{3}{2}}\) geeft \(q = -3\)

Samenvallen, dus \(p = 5\) en \(q = -3 \text{.}\)

\(k \perp l \text{,}\) dus \(l{:}\,-x - 4 y = c \text{.}\)

\(\begin{rcases}-x - 4 y = c \\ \text{door } A (-2 , -8)\end{rcases} c = -1 ⋅ -2 - 4 ⋅ -8 = 34\)
Dus \(l{:}\,-x - 4 y = 34 \text{.}\)