How many solutions does the system of equations below have?

y = –10x − 5
y
=
–7
4
x
+
1
8

The system of equations has no solutions because the slope of the first equation is -10 and the slope of the second equation is -7/4 which are not equal. This means the lines are parallel and will never intersect.

How many solutions does the system of equations below have?

y
=
5
4
x
− 4

y
=
8
7
x

7
5

The system of equations has no solutions because the slopes of the two equations are 5/4 and 8/7, which are different. This means the lines are not parallel but they will never intersect because they have different slopes.