one solution, infinitely many solutions, or no solution

Question

tell whether the system has one solution, infinitely many solutions, or no solution

17=11y+12x

12x+11y=13

Answer 1

The graph of y = mx + b is a straight line with slope m and y-intercept b.

 

If 17 = 11y + 12x, then 11y = -12x + 17

 

                                     So, y = (-12/11)x + 17/11

 

If 12x + 11y = 13, then 11y = -12x + 13

 

                                     So, y = (-12/11)x + 13/11

 

The first line has slope -12/11 and y-intercept 17/11.  The second line has slope -12/11 and y-interecept 13/11.

 

Since the lines have the same slope but different y-intercepts, the lines are parallel.  Therefore, the lines never intersect so the system has no solution.     

Answer 2

17 = 11y + 12x

12x + 11y = 13

 

Subtract the second equation from the first:

 

   11y + 12x  = 17

- (11y + 12x = 13)

------------------------

     0  +  0  =  4

     0 = 4

 

No solutions.  The two lines are parallel, so they never cross.