The line l contains the points A(4, 5) and B(2, 0) - Leaving Cert Mathematics - Question 4 - 2016

To find the intersection of lines l and k, we can substitute the equation from line k into line l:

1. Start with line k: $x + 2y = 8$ Rearranging gives: $2y = 8 - x \quad \Rightarrow y = 4 - \frac{1}{2}x$

2. Substitute into line l: $5x - 2y + 10 = 0$ Replace y with our expression from line k: $5x - 2(4 - \frac{1}{2}x) + 10 = 0$ $5x - 8 + x + 10 = 0$ $6x + 2 = 0 \Rightarrow x = -\frac{1}{3}$

Substituting x back into the equation for y: $y = 4 - \frac{1}{2}(-\frac{1}{3}) = 4 + \frac{1}{6} = \frac{24 + 1}{6} = \frac{25}{6}$

Thus, the intersection point l ∩ k is:

$(3, 2)$