Question

In a system of two linear equations, the lines represented by each equation have the same slope and different y-intercepts. Which would be the total number of solutions to the system of equations?

Answer 1

There will be no common solution

Explanation:

Given that the lines that represent the equations in the system of the two linear equations have equal slope but that their y-intercept are different, we have;

The two lines are parallel to each other

The two lines are different lines, given that they have different y-intercept

By definition of parallel lines, we have that the two lines representing the two equations will never meet, and therefore, both equations do not have a common solution which is a value that satisfies both equations

Therefore, the two equations in the linear system of equations, do not have a common solution