Jake and Erica were solving a system of equations. They both noticed that the two lines had the same slope. Jake said that because each line in the system had the same slope, the two lines had to be the same, which meant there were infinitely as many solutions to the system. Erica disagreed, and said they should also look at the y-intercepts before determining how many solutions there were. Who is correct?

A. Erica is correct. Two lines with equal slopes could be the same line, but only if they have the same y-intercept.

B. Jake is correct. Two lines with the same slope must be the same.

Question

Jake and Erica were solving a system of equations. They both noticed that the two lines had the same slope. Jake said that because each line in the system had the same slope, the two lines had to be the same, which meant there were infinitely as many solutions to the system. Erica disagreed, and said they should also look at the y-intercepts before determining how many solutions there were. Who is correct?

A. Erica is correct. Two lines with equal slopes could be the same line, but only if they have the same y-intercept.

B. Jake is correct. Two lines with the same slope must be the same.

anonymous · Answer

or C. Neither person makes a valid argument.

anonymous · Answer

The lines are not one in the same, but if they have the same slope but different y intercepts then it means that the two lines are parallel.

anonymous · Answer

so, C.

anonymous · Answer

thanks @pished17 !