Question

4. How many solutions does the system of equations have?

y= 5x + 7 and y= 5x + 8

A) one
B)two
C)none
D)infinitely many

Answer 1

C) none

Explanation:

The two lines are parallel (have the same slope (x-coefficient), but different y-intercepts). They have no point in common, hence there is no solution to the system of equations.

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Another way to think about this: subtract the first equation from the second. You get ...

0 = 1

There are no values of the variables that will make this be true, hence no solutions.