how many solutions exist for the system of equations below?

3x+y=18
3x+y=16

none
one
two
infinite

The correct option is 1.

Step-by-step explanation:

The system of equation is

A system of equation has two equation and .

1. If , then system of equations has no solution.

2. If , then system of equations has infinite solution.

3. If , then system of equation has one solution.

In the given system of equations,

Since , therefore the system of equation has no solution.

The correct option is 1.

the correct answer is option c.   3

step-by-step explanation:

points to remember

equation of the line with coordinates (x₁, y₁) and (x₂, y₂) is given by,

slope m = (y₂ - y₁)/(x₂ - x₁)

from the figure we can see a line with two coordinates given

to find the slope of given line

here   (x₁, y₁)   = (-1, -1 ) and (x₂, y₂) = (1, 5)

slope m = (y₂ - y₁)/(x₂ - x₁)

  = (5 - -1)/(1 - -1)

  = (5 + 1)/(1 + 1)

  = 6/2 = 3

therefore the correct answer is option c.   3