Question

How many solutions does the system have? \begin{cases} 3x+y=8 \\\\ 2x+2y=8 \end{cases} ⎩ ⎪ ⎪ ⎨ ⎪ ⎪ ⎧ ​ 3x+y=8 2x+2y=8 ​ Choose 1 answer: Choose 1 answer: (Choice A, Checked) A Exactly one solution (Choice B) B No solutions (Choice C) C Infinitely many solutions

Answer 1

Answer:

This system has one solution (x=2 and y=2), then the answer is A.

Step-by-step explanation:

The system of equations is:

$3x+y=8$ (1)

$2x+2y=8$ (2)

Let's multiply the first equation by 2 and subtract it to the second equation  

$6x-2x+2y-2y=16-8$

$4x=8$  

$x=2$

Using this value in (1) we can find y.

$3(2)+y=8$

$6+y=8$

$y=2$

Therefore, this system has one solution (x=2 and y=2), the answer is A.

I hope it helps you!