QuestionChoose $h$ and $k$ for the system to have (a) no solution, (b) a unique solution, and (c) many solutions. $$\begin{array}{r} x_{1}+h x_{2}=5 \\ 4 x_{1}+8 x_{2}=k \end{array}$$

Studdy Solution
(c) For the system to have many solutions, the two lines must coincide, which means they are the same line. This happens when $h=0$ and $k=20$.So, the correct choices area. The system has no solutions only when $h=0$ and $k\neq20$. b. The system has a unique solution only when $h\neq0$ and $k\neq20$. c. The system has many solutions only when $h=0$ and $k=20$.