A system of equations consists of two lines. One line passes through (-1, 3) and (0, 1). The other line passes through (1, 4) and (0, 2). Determine of the system has no solution, one solution, or an infinite number of solutions.

The equation of the line in its generic form is:

y = mx + b

Where,

m = (y2-y1) / (x2-x1)

For (-1, 3) and (0, 1):

We look for the value of m:

m = (1-3) / (0 - ( - 1))

m = ( - 2) / (0 + 1)

m = - 2

We look for the value of b:

1 = m (0) + b

b = 1

The line is:

y = - 2x + 1

For (1, 4) and (0, 2):

We look for the value of m:

m = (2-4) / (0-1)

m = ( - 2) / ( - 1)

m = 2

We look for the value of b:

2 = m (0) + b

b = 2

The line is:

y = 2x + 2

The system of equations is:

y = - 2x + 1

y = 2x + 2

Answer:

the system has one solution