$$2x − y = 5\ , \ 4x − 2y = t$$
(a) Determine a value of $t$ so that the system has a solution.
(b) Determine a value of $t$ so that the system has no solution.
What is the standard way to solve such questions?
$$2x − y = 5\ , \ 4x − 2y = t$$
(a) Determine a value of $t$ so that the system has a solution.
(b) Determine a value of $t$ so that the system has no solution.
What is the standard way to solve such questions?
Hints.
(a) Assign a value to $x$, compute $y$ from $2x-y=5$ and calculate $t=4x -2y$.
(b) Note that if you multiply the first equation by $2$, we obtain $4x − 2y = 10$.