Question

question 5 of 10
megan and sam were solving a system of equations. they both noticed that
the two lines had different slopes. megan said that because each line in the
system had different slopes, the 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-intercepts. who is correct?

a. neither person makes a valid argument.

b. sam is correct. when two lines intersect, their y-intercepts
determine how many solutions there will be.

c. megan is correct. when two lines have different slopes, they must
intersect, producing one solution.

Explanation:

To determine who is correct, we analyze the properties of linear equations. For two lines in a plane, if they have different slopes, they are not parallel (parallel lines have equal slopes) and thus must intersect at exactly one point. This means the system of equations (represented by the two lines) has one solution. The y - intercepts do not affect whether two lines with different slopes intersect; they only affect the point of intersection. So Megan's argument is valid, and Sam's is not (since the number of solutions for lines with different slopes is determined by the fact they intersect, not by the y - intercepts).

Answer:

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