Mathematics

Problem

Two walking paths in a park are represented on the coordinate plane by the following equations:

\begin{aligned}x+2y&=10,\\5x-y&=8.\end{aligned}

The park designer plans to set up a bench at point

P(2,4)

. a. (i) Verify whether point

P

satisfies the first equation. b. (ii) Verify whether point

P

satisfies the second equation. c. (iii) Decide whether

P

lies at the intersection of the two paths. Give a reason for your answer. d. (iv) Keeping the

x

–coordinate fixed at

2

, determine the

y

–coordinate so that the new point lies on both paths.