Question

question 6 of 10
matt and brian were solving a system of equations. they both noticed that the two lines had the same slope. brian said that because each line in the system had the same slope, the two lines had to be parallel, which meant the solution to the system was
o solutions.\ matt disagreed, and said they should also look at the y - intercepts before determining how many solutions there were. who is correct?
a. brian is correct. when two lines have the same slope, they are always parallel.
b. neither person makes a valid argument.
c. matt is correct. though two lines with equal slopes are often parallel, if they have the same y - intercept, they are the same line and have infinitely many solutions.

Explanation:

When two lines have the same slope:

• If they have different \(y\) - intercepts, they are parallel (no solutions).
• If they have the same \(y\) - intercept, they are the same line (infinitely many solutions).

So, Matt is correct as we need to check \(y\) - intercepts too.

Answer:

C. Matt is correct. Though two lines with equal slopes are often parallel, if they have the same \(y\) - intercept, they are the same line and have infinitely many solutions.