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.
Accepted Solution
A:
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