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