Question

How many solutions exist for the system of equations below? 3x+y=18 3x+y=16

Answer 1

A) 3x+y=18
B) 3x+y=16

These equations are inconsistent and have no solutions.  If these equations were graphed, it would be two parallel lines.

Answer 2

we have

$3x+y=18$ -------> equation $1$

solve for y

$y=-3x+18$

The slope $m=-3$

$3x+y=16$ -------> equation $2$

solve for y

$y=-3x+6$

The slope $m=-3$

The two slopes are the same, so the lines are parallel.

therefore

It's an inconsistent system of equations that has no solution.

the answer is

The system has no solution