Question

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.

Answer 1

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