Solve the following system of equations by graphing

Question

Solve the following system of equations by graphing. If the system is inconsistent or the equations are? dependent, say so,  and what are the solution set?

4x - 3y =1
8x - 6y =2

Answer 1

Given:

  4x - 3y =1
  8x - 6y =2     which is the same as:  4x - 3y =2     [note: divide by 2]

 

To solve by graphing:  Realize that two points define a line.  It is usually easy to find the y-intercept (the place where x=0) and the x-intercept (the place where y=0) and to draw the line through them.

                   

                           y-intercept             x-intercept

4x - 3y =1             (0, -1/3)                   (1/4, 0)
8x - 6y =2             (0, -1/3)                   (1/4, 0)

 

These are equivalent equations. The lines are actually the same line, and they 'cross' at infinitely many points (every point on the line). In this case, there are infinitely many solutions and the system is called dependent.