Question

How many solutions are there for the system of equations containing y = x-5 and

2x - 2y = 8, and why?

Answer 1

None, because 0 cannot equal 1.

Explanation:

y = x - 5

2x - 2y = 8

First let's solve for y in the bottom equation

Subtract 2x form both sides

2x - 2y = 8

- 2x - 2x

-2y = 8 - 2x

Divide both sides by -2

-2y/-2 = (8 - 2x)/-2

y = x - 4

Now substitute the y's in both equations

x - 4 = x - 5

Move like terms to one side by adding 4 to both sides

x - 4 = x - 5

+ 4 + 4

x = x - 1

Subtract x from both sides

x = x - 1

- x - x

0 = 1

Zero cannot equal one, meaning this system of equations is invalid and has no solutions.