Business Calc Question

Question

Given the lines:

y = 3x + 5
y = 3x - 6

will this system have a solution? How can you tell without solving the system?

Answer 1

The graph of y = mx+b is a line with slope m and y-intercept (0,b).

 

So, the lines y = 3x+5 and y = 3x-6 have the same slope (3) and different y-intercepts [(0,5) and (0,-6)].

 

   Therefore, the lines do not intersect.  (i.e., the system has no solution)