which of the linear systwms has exactly one solution?

Question

A. y=3x-5  y=3x+5

 

B. y=3x+6  y=3(x+2)

 

C. y=3x+4  y=3x-7

 

D. y=3x-1  y=-3x+1

 

Please show steps.

Answer 1

In A., B., and C. the slopes of both equations is 3. The lines are parallel and do not intersect. They do not have a common solution.

 

D. is the only option left.

The slopes are different. Therefore they intersect and have one common solution.