Mathematics

Problem

Consider the pair of equations involving the parameter

k

\begin{aligned}(k+1)x+2y&=7,\\3x+(k-4)y&=5.\end{aligned}

The ordered pair

S(1,2)

is suggested as a common solution. a. (i) Substitute

S

in the first equation and obtain the resulting condition on

k

. b. (ii) Substitute

S

in the second equation and obtain the resulting condition on

k

. c. (iii) Solve the conditions obtained in (i) and (ii) to find the value(s) of

k

for which

S

satisfies both equations simultaneously. d. (iv) For the value(s) of

k

found in (iii), verify explicitly that

S

satisfies each of the given equations.