Question

Megan and Sam were solving a system of equations they both noticed that those two lines had different slopes Megan said that because each line in the system had different slope two lines had to intersect which meant there was one solution to the system Sam disagreed and said they should also look at the y intercept who is correct?

Answer 1

Correct answer: Megan is correct. When two lines have different slopes, they must intersect producing one solution.

Explanation:

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Answer 2

Megan is correct.

Explanation:

Since, a system of two lines has,

No solution : When both lines have the same slope but different x-intercept and y -intercept.

Infinitely many solution : When both lines have the same slope and same x-intercept and y -intercept.

One solution : When both lines have different slopes,

Since, here it is given that the lines have the different slope,

Thus, it is clear that the system of equation has only one solution,

And, we do not need to check the y-intercept.

Hence, Megan is correct.