Question

How many solutions does the system have? You can use the interactive graph below to find the answer. \begin{cases} 4x-2y=8 \\\\ 2x+y=2 \end{cases} ⎩ ⎪ ⎪ ⎨ ⎪ ⎪ ⎧ ​ 4x−2y=8 2x+y=2 ​ Choose 1 answer: Choose 1 answer: (Choice A) A Exactly one solution (Choice B) B No solutions (Choice C) C Infinitely many solutions

Answer 1

$\Huge\boxed{\textsf{A. Exactly one solution}}$

We have the following system:

$\begin{cases}4x-2y&=8\\2x+y&=2\end{cases}$

Here, a simple solution to find the answer is to graph the two lines and see how many times they intersect.

I've attached a graph, with $4x-2y=8$ in red and the other equation in blue.

See that the lines only intersect once, at $(1.5,-1)$. This means the system only has one solution.