How many solutions are there for the system of equations containing y = x – 5 and 2x – 2y = 8, and why?

Answer 1

Doing a few slight manipulations on 2x – 2y = 8 (adding 2y to both sides, subtracting 8 from both sides, and dividing both sides by 2) we get:

2x – 2y = 8

2x = 2y + 8

2x -8 = 2y

x - 4 = y

Comparing the two equations now we have:

y = x - 5 and y = x - 4

These are two parallel lines because the slope of both is "1" and they have different y-intercept (one is "-5" and the other is "-4") so there are NO solutions (the lines never intersect).

Answer 2

y = x - 5

2x - 2y = 8

-2y = -2x + 8

y = x - 4

The two lines are parallel with different y-intercepts.

The do not intersect. They do not have a common point.

The equations do not have a common solution